[{"author":[{"first_name":"Mengyao","last_name":"Ding","full_name":"Ding, Mengyao"},{"first_name":"Michael","full_name":"Winkler, Michael","id":"31496","last_name":"Winkler"}],"date_created":"2025-12-18T19:04:45Z","volume":37,"date_updated":"2025-12-18T20:13:49Z","publisher":"IOP Publishing","doi":"10.1088/1361-6544/ad871a","title":"Radial blow-up in quasilinear Keller-Segel systems: approaching the full picture","issue":"12","publication_status":"published","publication_identifier":{"issn":["0951-7715","1361-6544"]},"citation":{"apa":"Ding, M., &#38; Winkler, M. (2024). Radial blow-up in quasilinear Keller-Segel systems: approaching the full picture. <i>Nonlinearity</i>, <i>37</i>(12), Article 125006. <a href=\"https://doi.org/10.1088/1361-6544/ad871a\">https://doi.org/10.1088/1361-6544/ad871a</a>","short":"M. Ding, M. Winkler, Nonlinearity 37 (2024).","bibtex":"@article{Ding_Winkler_2024, title={Radial blow-up in quasilinear Keller-Segel systems: approaching the full picture}, volume={37}, DOI={<a href=\"https://doi.org/10.1088/1361-6544/ad871a\">10.1088/1361-6544/ad871a</a>}, number={12125006}, journal={Nonlinearity}, publisher={IOP Publishing}, author={Ding, Mengyao and Winkler, Michael}, year={2024} }","mla":"Ding, Mengyao, and Michael Winkler. “Radial Blow-up in Quasilinear Keller-Segel Systems: Approaching the Full Picture.” <i>Nonlinearity</i>, vol. 37, no. 12, 125006, IOP Publishing, 2024, doi:<a href=\"https://doi.org/10.1088/1361-6544/ad871a\">10.1088/1361-6544/ad871a</a>.","chicago":"Ding, Mengyao, and Michael Winkler. “Radial Blow-up in Quasilinear Keller-Segel Systems: Approaching the Full Picture.” <i>Nonlinearity</i> 37, no. 12 (2024). <a href=\"https://doi.org/10.1088/1361-6544/ad871a\">https://doi.org/10.1088/1361-6544/ad871a</a>.","ieee":"M. Ding and M. Winkler, “Radial blow-up in quasilinear Keller-Segel systems: approaching the full picture,” <i>Nonlinearity</i>, vol. 37, no. 12, Art. no. 125006, 2024, doi: <a href=\"https://doi.org/10.1088/1361-6544/ad871a\">10.1088/1361-6544/ad871a</a>.","ama":"Ding M, Winkler M. Radial blow-up in quasilinear Keller-Segel systems: approaching the full picture. <i>Nonlinearity</i>. 2024;37(12). doi:<a href=\"https://doi.org/10.1088/1361-6544/ad871a\">10.1088/1361-6544/ad871a</a>"},"intvolume":"        37","year":"2024","user_id":"31496","_id":"63253","language":[{"iso":"eng"}],"article_number":"125006","type":"journal_article","publication":"Nonlinearity","status":"public","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title>\r\n               <jats:p>The Neumann problem for the Keller-Segel system <jats:inline-formula>\r\n                     <jats:tex-math/>\r\n                     <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\">\r\n                        <mml:mrow>\r\n                           <mml:mtable columnalign=\"left\" displaystyle=\"true\">\r\n                              <mml:mtr>\r\n                                 <mml:mtd>\r\n                                    <mml:mrow>\r\n                                       <mml:mo>{</mml:mo>\r\n                                       <mml:mtable columnalign=\"left\" displaystyle=\"true\">\r\n                                          <mml:mtr>\r\n                                             <mml:mtd>\r\n                                                <mml:msub>\r\n                                                   <mml:mi>u</mml:mi>\r\n                                                   <mml:mi>t</mml:mi>\r\n                                                </mml:msub>\r\n                                                <mml:mo>=</mml:mo>\r\n                                                <mml:mi mathvariant=\"normal\">∇</mml:mi>\r\n                                                <mml:mo>⋅</mml:mo>\r\n                                                <mml:mrow>\r\n                                                   <mml:mo>(</mml:mo>\r\n                                                   <mml:mi>D</mml:mi>\r\n                                                   <mml:mrow>\r\n                                                      <mml:mo>(</mml:mo>\r\n                                                      <mml:mi>u</mml:mi>\r\n                                                      <mml:mo>)</mml:mo>\r\n                                                   </mml:mrow>\r\n                                                   <mml:mi mathvariant=\"normal\">∇</mml:mi>\r\n                                                   <mml:mi>u</mml:mi>\r\n                                                   <mml:mo>)</mml:mo>\r\n                                                </mml:mrow>\r\n                                                <mml:mo>−</mml:mo>\r\n                                                <mml:mi mathvariant=\"normal\">∇</mml:mi>\r\n                                                <mml:mo>⋅</mml:mo>\r\n                                                <mml:mrow>\r\n                                                   <mml:mo>(</mml:mo>\r\n                                                   <mml:mi>S</mml:mi>\r\n                                                   <mml:mrow>\r\n                                                      <mml:mo>(</mml:mo>\r\n                                                      <mml:mi>u</mml:mi>\r\n                                                      <mml:mo>)</mml:mo>\r\n                                                   </mml:mrow>\r\n                                                   <mml:mi mathvariant=\"normal\">∇</mml:mi>\r\n                                                   <mml:mi>v</mml:mi>\r\n                                                   <mml:mo>)</mml:mo>\r\n                                                </mml:mrow>\r\n                                                <mml:mo>,</mml:mo>\r\n                                             </mml:mtd>\r\n                                          </mml:mtr>\r\n                                          <mml:mtr>\r\n                                             <mml:mtd>\r\n                                                <mml:mn>0</mml:mn>\r\n                                                <mml:mo>=</mml:mo>\r\n                                                <mml:mi mathvariant=\"normal\">Δ</mml:mi>\r\n                                                <mml:mi>v</mml:mi>\r\n                                                <mml:mo>−</mml:mo>\r\n                                                <mml:mi>μ</mml:mi>\r\n                                                <mml:mo>+</mml:mo>\r\n                                                <mml:mi>u</mml:mi>\r\n                                                <mml:mo>,</mml:mo>\r\n                                                <mml:mstyle scriptlevel=\"0\"/>\r\n                                                <mml:mi>μ</mml:mi>\r\n                                                <mml:mo>=</mml:mo>\r\n                                                <mml:mstyle displaystyle=\"true\" scriptlevel=\"0\">\r\n                                                   <mml:mo>−</mml:mo>\r\n                                                   <mml:mstyle scriptlevel=\"0\"/>\r\n                                                   <mml:mstyle scriptlevel=\"0\"/>\r\n                                                   <mml:mstyle scriptlevel=\"0\"/>\r\n                                                   <mml:mstyle scriptlevel=\"0\"/>\r\n                                                   <mml:mstyle scriptlevel=\"0\"/>\r\n                                                   <mml:mstyle scriptlevel=\"0\"/>\r\n                                                   <mml:mstyle scriptlevel=\"0\"/>\r\n                                                   <mml:mstyle scriptlevel=\"0\"/>\r\n                                                   <mml:mstyle scriptlevel=\"0\"/>\r\n                                                   <mml:msub>\r\n                                                      <mml:mo>∫</mml:mo>\r\n                                                      <mml:mi mathvariant=\"normal\">Ω</mml:mi>\r\n                                                   </mml:msub>\r\n                                                   <mml:mi>u</mml:mi>\r\n                                                   <mml:mtext>d</mml:mtext>\r\n                                                   <mml:mi>x</mml:mi>\r\n                                                   <mml:mo>,</mml:mo>\r\n                                                </mml:mstyle>\r\n                                             </mml:mtd>\r\n                                          </mml:mtr>\r\n                                       </mml:mtable>\r\n                                    </mml:mrow>\r\n                                 </mml:mtd>\r\n                              </mml:mtr>\r\n                           </mml:mtable>\r\n                        </mml:mrow>\r\n                     </mml:math>\r\n                  </jats:inline-formula> is considered in <jats:italic>n</jats:italic>-dimensional balls Ω with <jats:inline-formula>\r\n                     <jats:tex-math/>\r\n                     <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\">\r\n                        <mml:mrow>\r\n                           <mml:mi>n</mml:mi>\r\n                           <mml:mtext>⩾</mml:mtext>\r\n                           <mml:mn>2</mml:mn>\r\n                        </mml:mrow>\r\n                     </mml:math>\r\n                  </jats:inline-formula>, with suitably regular and radially symmetric, radially nonincreasing initial data <jats:italic>u</jats:italic>\r\n                  <jats:sub>0</jats:sub>. The functions <jats:italic>D</jats:italic> and <jats:italic>S</jats:italic> are only assumed to belong to <jats:inline-formula>\r\n                     <jats:tex-math/>\r\n                     <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\">\r\n                        <mml:mrow>\r\n                           <mml:msup>\r\n                              <mml:mi>C</mml:mi>\r\n                              <mml:mn>2</mml:mn>\r\n                           </mml:msup>\r\n                           <mml:mo stretchy=\"false\">(</mml:mo>\r\n                           <mml:mo stretchy=\"false\">[</mml:mo>\r\n                           <mml:mn>0</mml:mn>\r\n                           <mml:mo>,</mml:mo>\r\n                           <mml:mi mathvariant=\"normal\">∞</mml:mi>\r\n                           <mml:mo stretchy=\"false\">)</mml:mo>\r\n                           <mml:mo stretchy=\"false\">)</mml:mo>\r\n                        </mml:mrow>\r\n                     </mml:math>\r\n                  </jats:inline-formula> and to satisfy <jats:italic>D</jats:italic> &gt; 0 and <jats:inline-formula>\r\n                     <jats:tex-math/>\r\n                     <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\">\r\n                        <mml:mrow>\r\n                           <mml:mi>S</mml:mi>\r\n                           <mml:mtext>⩾</mml:mtext>\r\n                           <mml:mn>0</mml:mn>\r\n                        </mml:mrow>\r\n                     </mml:math>\r\n                  </jats:inline-formula> on <jats:inline-formula>\r\n                     <jats:tex-math/>\r\n                     <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\">\r\n                        <mml:mrow>\r\n                           <mml:mo stretchy=\"false\">[</mml:mo>\r\n                           <mml:mn>0</mml:mn>\r\n                           <mml:mo>,</mml:mo>\r\n                           <mml:mi mathvariant=\"normal\">∞</mml:mi>\r\n                           <mml:mo stretchy=\"false\">)</mml:mo>\r\n                        </mml:mrow>\r\n                     </mml:math>\r\n                  </jats:inline-formula> as well as <jats:inline-formula>\r\n                     <jats:tex-math/>\r\n                     <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\">\r\n                        <mml:mrow>\r\n                           <mml:mi>S</mml:mi>\r\n                           <mml:mo stretchy=\"false\">(</mml:mo>\r\n                           <mml:mn>0</mml:mn>\r\n                           <mml:mo stretchy=\"false\">)</mml:mo>\r\n                           <mml:mo>=</mml:mo>\r\n                           <mml:mn>0</mml:mn>\r\n                        </mml:mrow>\r\n                     </mml:math>\r\n                  </jats:inline-formula>; in particular, diffusivities with arbitrarily fast decay are included.</jats:p>\r\n               <jats:p>In this general context, it is shown that it is merely the asymptotic behavior as <jats:inline-formula>\r\n                     <jats:tex-math/>\r\n                     <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\">\r\n                        <mml:mrow>\r\n                           <mml:mi>ξ</mml:mi>\r\n                           <mml:mo accent=\"false\" stretchy=\"false\">→</mml:mo>\r\n                           <mml:mi mathvariant=\"normal\">∞</mml:mi>\r\n                        </mml:mrow>\r\n                     </mml:math>\r\n                  </jats:inline-formula> of the expression <jats:inline-formula>\r\n                     <jats:tex-math/>\r\n                     <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\">\r\n                        <mml:mrow>\r\n                           <mml:mtable columnalign=\"left\" displaystyle=\"true\">\r\n                              <mml:mtr>\r\n                                 <mml:mtd>\r\n                                    <mml:mi>I</mml:mi>\r\n                                    <mml:mrow>\r\n                                       <mml:mo>(</mml:mo>\r\n                                       <mml:mi>ξ</mml:mi>\r\n                                       <mml:mo>)</mml:mo>\r\n                                    </mml:mrow>\r\n                                    <mml:mo>:=</mml:mo>\r\n                                    <mml:mfrac>\r\n                                       <mml:mrow>\r\n                                          <mml:mi>S</mml:mi>\r\n                                          <mml:mrow>\r\n                                             <mml:mo>(</mml:mo>\r\n                                             <mml:mi>ξ</mml:mi>\r\n                                             <mml:mo>)</mml:mo>\r\n                                          </mml:mrow>\r\n                                       </mml:mrow>\r\n                                       <mml:mrow>\r\n                                          <mml:msup>\r\n                                             <mml:mi>ξ</mml:mi>\r\n                                             <mml:mfrac>\r\n                                                <mml:mn>2</mml:mn>\r\n                                                <mml:mi>n</mml:mi>\r\n                                             </mml:mfrac>\r\n                                          </mml:msup>\r\n                                          <mml:mi>D</mml:mi>\r\n                                          <mml:mrow>\r\n                                             <mml:mo>(</mml:mo>\r\n                                             <mml:mi>ξ</mml:mi>\r\n                                             <mml:mo>)</mml:mo>\r\n                                          </mml:mrow>\r\n                                       </mml:mrow>\r\n                                    </mml:mfrac>\r\n                                    <mml:mo>,</mml:mo>\r\n                                    <mml:mstyle scriptlevel=\"0\"/>\r\n                                    <mml:mi>ξ</mml:mi>\r\n                                    <mml:mo>&gt;</mml:mo>\r\n                                    <mml:mn>0</mml:mn>\r\n                                    <mml:mo>,</mml:mo>\r\n                                 </mml:mtd>\r\n                              </mml:mtr>\r\n                           </mml:mtable>\r\n                        </mml:mrow>\r\n                     </mml:math>\r\n                  </jats:inline-formula> which decides about the occurrence of blow-up: Namely, it is seen that\r\n<jats:list id=\"nonad871al1\" list-type=\"bullet\">\r\n                     <jats:list-item id=\"nonad871al1.1\">\r\n                        <jats:label>•</jats:label>\r\n                        <jats:p>if <jats:inline-formula>\r\n                              <jats:tex-math/>\r\n                              <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\">\r\n                                 <mml:mrow>\r\n                                    <mml:munder>\r\n                                       <mml:mo movablelimits=\"true\">lim</mml:mo>\r\n                                       <mml:mrow>\r\n                                          <mml:mi>ξ</mml:mi>\r\n                                          <mml:mo accent=\"false\" stretchy=\"false\">→</mml:mo>\r\n                                          <mml:mi mathvariant=\"normal\">∞</mml:mi>\r\n                                       </mml:mrow>\r\n                                    </mml:munder>\r\n                                    <mml:mi>I</mml:mi>\r\n                                    <mml:mo stretchy=\"false\">(</mml:mo>\r\n                                    <mml:mi>ξ</mml:mi>\r\n                                    <mml:mo stretchy=\"false\">)</mml:mo>\r\n                                    <mml:mo>=</mml:mo>\r\n                                    <mml:mn>0</mml:mn>\r\n                                 </mml:mrow>\r\n                              </mml:math>\r\n                           </jats:inline-formula>, then any such solution is global and bounded, that</jats:p>\r\n                     </jats:list-item>\r\n                     <jats:list-item id=\"nonad871al1.2\">\r\n                        <jats:label>•</jats:label>\r\n                        <jats:p>if <jats:inline-formula>\r\n                              <jats:tex-math/>\r\n                              <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\">\r\n                                 <mml:mrow>\r\n                                    <mml:munder>\r\n                                       <mml:mo movablelimits=\"true\">lim sup</mml:mo>\r\n                                       <mml:mrow>\r\n                                          <mml:mi>ξ</mml:mi>\r\n                                          <mml:mo accent=\"false\" stretchy=\"false\">→</mml:mo>\r\n                                          <mml:mi mathvariant=\"normal\">∞</mml:mi>\r\n                                       </mml:mrow>\r\n                                    </mml:munder>\r\n                                    <mml:mi>I</mml:mi>\r\n                                    <mml:mo stretchy=\"false\">(</mml:mo>\r\n                                    <mml:mi>ξ</mml:mi>\r\n                                    <mml:mo stretchy=\"false\">)</mml:mo>\r\n                                    <mml:mo>&lt;</mml:mo>\r\n                                    <mml:mi mathvariant=\"normal\">∞</mml:mi>\r\n                                 </mml:mrow>\r\n                              </mml:math>\r\n                           </jats:inline-formula> and <jats:inline-formula>\r\n                              <jats:tex-math/>\r\n                              <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\">\r\n                                 <mml:mrow>\r\n                                    <mml:msub>\r\n                                       <mml:mo>∫</mml:mo>\r\n                                       <mml:mi mathvariant=\"normal\">Ω</mml:mi>\r\n                                    </mml:msub>\r\n                                    <mml:msub>\r\n                                       <mml:mi>u</mml:mi>\r\n                                       <mml:mn>0</mml:mn>\r\n                                    </mml:msub>\r\n                                 </mml:mrow>\r\n                              </mml:math>\r\n                           </jats:inline-formula> is suitably small, then the corresponding solution is global and bounded, and that</jats:p>\r\n                     </jats:list-item>\r\n                     <jats:list-item id=\"nonad871al1.3\">\r\n                        <jats:label>•</jats:label>\r\n                        <jats:p>if <jats:inline-formula>\r\n                              <jats:tex-math/>\r\n                              <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\">\r\n                                 <mml:mrow>\r\n                                    <mml:munder>\r\n                                       <mml:mo movablelimits=\"true\">lim inf</mml:mo>\r\n                                       <mml:mrow>\r\n                                          <mml:mi>ξ</mml:mi>\r\n                                          <mml:mo accent=\"false\" stretchy=\"false\">→</mml:mo>\r\n                                          <mml:mi mathvariant=\"normal\">∞</mml:mi>\r\n                                       </mml:mrow>\r\n                                    </mml:munder>\r\n                                    <mml:mi>I</mml:mi>\r\n                                    <mml:mo stretchy=\"false\">(</mml:mo>\r\n                                    <mml:mi>ξ</mml:mi>\r\n                                    <mml:mo stretchy=\"false\">)</mml:mo>\r\n                                    <mml:mo>&gt;</mml:mo>\r\n                                    <mml:mn>0</mml:mn>\r\n                                 </mml:mrow>\r\n                              </mml:math>\r\n                           </jats:inline-formula>, then at each appropriately large mass level <jats:italic>m</jats:italic>, there exist radial initial data <jats:italic>u</jats:italic>\r\n                           <jats:sub>0</jats:sub> such that <jats:inline-formula>\r\n                              <jats:tex-math/>\r\n                              <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\">\r\n                                 <mml:mrow>\r\n                                    <mml:msub>\r\n                                       <mml:mo>∫</mml:mo>\r\n                                       <mml:mi mathvariant=\"normal\">Ω</mml:mi>\r\n                                    </mml:msub>\r\n                                    <mml:msub>\r\n                                       <mml:mi>u</mml:mi>\r\n                                       <mml:mn>0</mml:mn>\r\n                                    </mml:msub>\r\n                                    <mml:mo>=</mml:mo>\r\n                                    <mml:mi>m</mml:mi>\r\n                                 </mml:mrow>\r\n                              </mml:math>\r\n                           </jats:inline-formula>, and that the associated solution blows up either in finite or in infinite time.</jats:p>\r\n                     </jats:list-item>\r\n                  </jats:list>\r\n               </jats:p>\r\n               <jats:p>This especially reveals the presence of critical mass phenomena whenever <jats:inline-formula>\r\n                     <jats:tex-math/>\r\n                     <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\">\r\n                        <mml:mrow>\r\n                           <mml:munder>\r\n                              <mml:mo movablelimits=\"true\">lim</mml:mo>\r\n                              <mml:mrow>\r\n                                 <mml:mi>ξ</mml:mi>\r\n                                 <mml:mo accent=\"false\" stretchy=\"false\">→</mml:mo>\r\n                                 <mml:mi mathvariant=\"normal\">∞</mml:mi>\r\n                              </mml:mrow>\r\n                           </mml:munder>\r\n                           <mml:mi>I</mml:mi>\r\n                           <mml:mo stretchy=\"false\">(</mml:mo>\r\n                           <mml:mi>ξ</mml:mi>\r\n                           <mml:mo stretchy=\"false\">)</mml:mo>\r\n                           <mml:mo>∈</mml:mo>\r\n                           <mml:mo stretchy=\"false\">(</mml:mo>\r\n                           <mml:mn>0</mml:mn>\r\n                           <mml:mo>,</mml:mo>\r\n                           <mml:mi mathvariant=\"normal\">∞</mml:mi>\r\n                           <mml:mo stretchy=\"false\">)</mml:mo>\r\n                        </mml:mrow>\r\n                     </mml:math>\r\n                  </jats:inline-formula> exists.</jats:p>"}]},{"status":"public","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>The chemotaxis-Navier–Stokes system <jats:disp-formula><jats:alternatives><jats:tex-math>$$\\begin{aligned} \\left\\{ \\begin{array}{rcl} n_t+u\\cdot \\nabla n &amp; =&amp;  \\Delta \\big (n c^{-\\alpha } \\big ), \\\\ c_t+ u\\cdot \\nabla c &amp; =&amp;  \\Delta c -nc,\\\\ u_t + (u\\cdot \\nabla ) u &amp; =&amp; \\Delta u+\\nabla P + n\\nabla \\Phi , \\qquad \\nabla \\cdot u=0, \\end{array} \\right. \\end{aligned}$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mtable>\r\n                      <mml:mtr>\r\n                        <mml:mtd>\r\n                          <mml:mfenced>\r\n                            <mml:mrow>\r\n                              <mml:mtable>\r\n                                <mml:mtr>\r\n                                  <mml:mtd>\r\n                                    <mml:mrow>\r\n                                      <mml:msub>\r\n                                        <mml:mi>n</mml:mi>\r\n                                        <mml:mi>t</mml:mi>\r\n                                      </mml:msub>\r\n                                      <mml:mo>+</mml:mo>\r\n                                      <mml:mi>u</mml:mi>\r\n                                      <mml:mo>·</mml:mo>\r\n                                      <mml:mi>∇</mml:mi>\r\n                                      <mml:mi>n</mml:mi>\r\n                                    </mml:mrow>\r\n                                  </mml:mtd>\r\n                                  <mml:mtd>\r\n                                    <mml:mo>=</mml:mo>\r\n                                  </mml:mtd>\r\n                                  <mml:mtd>\r\n                                    <mml:mrow>\r\n                                      <mml:mi>Δ</mml:mi>\r\n                                      <mml:mrow>\r\n                                        <mml:mo>(</mml:mo>\r\n                                      </mml:mrow>\r\n                                      <mml:mi>n</mml:mi>\r\n                                      <mml:msup>\r\n                                        <mml:mi>c</mml:mi>\r\n                                        <mml:mrow>\r\n                                          <mml:mo>-</mml:mo>\r\n                                          <mml:mi>α</mml:mi>\r\n                                        </mml:mrow>\r\n                                      </mml:msup>\r\n                                      <mml:mrow>\r\n                                        <mml:mo>)</mml:mo>\r\n                                      </mml:mrow>\r\n                                      <mml:mo>,</mml:mo>\r\n                                    </mml:mrow>\r\n                                  </mml:mtd>\r\n                                </mml:mtr>\r\n                                <mml:mtr>\r\n                                  <mml:mtd>\r\n                                    <mml:mrow>\r\n                                      <mml:mrow/>\r\n                                      <mml:msub>\r\n                                        <mml:mi>c</mml:mi>\r\n                                        <mml:mi>t</mml:mi>\r\n                                      </mml:msub>\r\n                                      <mml:mo>+</mml:mo>\r\n                                      <mml:mi>u</mml:mi>\r\n                                      <mml:mo>·</mml:mo>\r\n                                      <mml:mi>∇</mml:mi>\r\n                                      <mml:mi>c</mml:mi>\r\n                                    </mml:mrow>\r\n                                  </mml:mtd>\r\n                                  <mml:mtd>\r\n                                    <mml:mo>=</mml:mo>\r\n                                  </mml:mtd>\r\n                                  <mml:mtd>\r\n                                    <mml:mrow>\r\n                                      <mml:mi>Δ</mml:mi>\r\n                                      <mml:mi>c</mml:mi>\r\n                                      <mml:mo>-</mml:mo>\r\n                                      <mml:mi>n</mml:mi>\r\n                                      <mml:mi>c</mml:mi>\r\n                                      <mml:mo>,</mml:mo>\r\n                                    </mml:mrow>\r\n                                  </mml:mtd>\r\n                                </mml:mtr>\r\n                                <mml:mtr>\r\n                                  <mml:mtd>\r\n                                    <mml:mrow>\r\n                                      <mml:mrow/>\r\n                                      <mml:msub>\r\n                                        <mml:mi>u</mml:mi>\r\n                                        <mml:mi>t</mml:mi>\r\n                                      </mml:msub>\r\n                                      <mml:mo>+</mml:mo>\r\n                                      <mml:mrow>\r\n                                        <mml:mo>(</mml:mo>\r\n                                        <mml:mi>u</mml:mi>\r\n                                        <mml:mo>·</mml:mo>\r\n                                        <mml:mi>∇</mml:mi>\r\n                                        <mml:mo>)</mml:mo>\r\n                                      </mml:mrow>\r\n                                      <mml:mi>u</mml:mi>\r\n                                    </mml:mrow>\r\n                                  </mml:mtd>\r\n                                  <mml:mtd>\r\n                                    <mml:mo>=</mml:mo>\r\n                                  </mml:mtd>\r\n                                  <mml:mtd>\r\n                                    <mml:mrow>\r\n                                      <mml:mi>Δ</mml:mi>\r\n                                      <mml:mi>u</mml:mi>\r\n                                      <mml:mo>+</mml:mo>\r\n                                      <mml:mi>∇</mml:mi>\r\n                                      <mml:mi>P</mml:mi>\r\n                                      <mml:mo>+</mml:mo>\r\n                                      <mml:mi>n</mml:mi>\r\n                                      <mml:mi>∇</mml:mi>\r\n                                      <mml:mi>Φ</mml:mi>\r\n                                      <mml:mo>,</mml:mo>\r\n                                      <mml:mspace/>\r\n                                      <mml:mi>∇</mml:mi>\r\n                                      <mml:mo>·</mml:mo>\r\n                                      <mml:mi>u</mml:mi>\r\n                                      <mml:mo>=</mml:mo>\r\n                                      <mml:mn>0</mml:mn>\r\n                                      <mml:mo>,</mml:mo>\r\n                                    </mml:mrow>\r\n                                  </mml:mtd>\r\n                                </mml:mtr>\r\n                              </mml:mtable>\r\n                            </mml:mrow>\r\n                          </mml:mfenced>\r\n                        </mml:mtd>\r\n                      </mml:mtr>\r\n                    </mml:mtable>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:disp-formula>modelling the behavior of aerobic bacteria in a fluid drop, is considered in a smoothly bounded domain <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\Omega \\subset \\mathbb R^2$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>Ω</mml:mi>\r\n                    <mml:mo>⊂</mml:mo>\r\n                    <mml:msup>\r\n                      <mml:mi>R</mml:mi>\r\n                      <mml:mn>2</mml:mn>\r\n                    </mml:msup>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>. For all <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\alpha &gt; 0$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>α</mml:mi>\r\n                    <mml:mo>&gt;</mml:mo>\r\n                    <mml:mn>0</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula> and all sufficiently regular <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\Phi $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mi>Φ</mml:mi>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, we construct global classical solutions and thereby extend recent results for the fluid-free analogue to the system coupled to a Navier–Stokes system. As a crucial new challenge, our analysis requires a priori estimates for <jats:italic>u</jats:italic> at a point in the proof when knowledge about <jats:italic>n</jats:italic> is essentially limited to the observation that the mass is conserved. To overcome this problem, we also prove new uniform-in-time <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^p$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:msup>\r\n                    <mml:mi>L</mml:mi>\r\n                    <mml:mi>p</mml:mi>\r\n                  </mml:msup>\r\n                </mml:math></jats:alternatives></jats:inline-formula> estimates for solutions to the inhomogeneous Navier–Stokes equations merely depending on the space-time <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^2$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:msup>\r\n                    <mml:mi>L</mml:mi>\r\n                    <mml:mn>2</mml:mn>\r\n                  </mml:msup>\r\n                </mml:math></jats:alternatives></jats:inline-formula> norm of the force term raised to an arbitrary small power.</jats:p>"}],"type":"journal_article","publication":"Journal of Mathematical Fluid Mechanics","language":[{"iso":"eng"}],"article_number":"60","user_id":"31496","_id":"63254","citation":{"apa":"Fuest, M., &#38; Winkler, M. (2024). Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing. <i>Journal of Mathematical Fluid Mechanics</i>, <i>26</i>(4), Article 60. <a href=\"https://doi.org/10.1007/s00021-024-00899-8\">https://doi.org/10.1007/s00021-024-00899-8</a>","mla":"Fuest, Mario, and Michael Winkler. “Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing.” <i>Journal of Mathematical Fluid Mechanics</i>, vol. 26, no. 4, 60, Springer Science and Business Media LLC, 2024, doi:<a href=\"https://doi.org/10.1007/s00021-024-00899-8\">10.1007/s00021-024-00899-8</a>.","short":"M. Fuest, M. Winkler, Journal of Mathematical Fluid Mechanics 26 (2024).","bibtex":"@article{Fuest_Winkler_2024, title={Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing}, volume={26}, DOI={<a href=\"https://doi.org/10.1007/s00021-024-00899-8\">10.1007/s00021-024-00899-8</a>}, number={460}, journal={Journal of Mathematical Fluid Mechanics}, publisher={Springer Science and Business Media LLC}, author={Fuest, Mario and Winkler, Michael}, year={2024} }","chicago":"Fuest, Mario, and Michael Winkler. “Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing.” <i>Journal of Mathematical Fluid Mechanics</i> 26, no. 4 (2024). <a href=\"https://doi.org/10.1007/s00021-024-00899-8\">https://doi.org/10.1007/s00021-024-00899-8</a>.","ieee":"M. Fuest and M. Winkler, “Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing,” <i>Journal of Mathematical Fluid Mechanics</i>, vol. 26, no. 4, Art. no. 60, 2024, doi: <a href=\"https://doi.org/10.1007/s00021-024-00899-8\">10.1007/s00021-024-00899-8</a>.","ama":"Fuest M, Winkler M. Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing. <i>Journal of Mathematical Fluid Mechanics</i>. 2024;26(4). doi:<a href=\"https://doi.org/10.1007/s00021-024-00899-8\">10.1007/s00021-024-00899-8</a>"},"intvolume":"        26","year":"2024","issue":"4","publication_status":"published","publication_identifier":{"issn":["1422-6928","1422-6952"]},"doi":"10.1007/s00021-024-00899-8","title":"Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing","date_created":"2025-12-18T19:05:09Z","author":[{"last_name":"Fuest","full_name":"Fuest, Mario","first_name":"Mario"},{"last_name":"Winkler","id":"31496","full_name":"Winkler, Michael","first_name":"Michael"}],"volume":26,"publisher":"Springer Science and Business Media LLC","date_updated":"2025-12-18T20:13:58Z"},{"doi":"10.1112/jlms.12885","title":"An interpolation inequality involving LlogL$L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system","author":[{"first_name":"Yulan","full_name":"Wang, Yulan","last_name":"Wang"},{"full_name":"Winkler, Michael","id":"31496","last_name":"Winkler","first_name":"Michael"}],"date_created":"2025-12-18T19:07:25Z","volume":109,"publisher":"Wiley","date_updated":"2025-12-18T20:14:39Z","citation":{"bibtex":"@article{Wang_Winkler_2024, title={An interpolation inequality involving LlogL$L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system}, volume={109}, DOI={<a href=\"https://doi.org/10.1112/jlms.12885\">10.1112/jlms.12885</a>}, number={3e12885}, journal={Journal of the London Mathematical Society}, publisher={Wiley}, author={Wang, Yulan and Winkler, Michael}, year={2024} }","mla":"Wang, Yulan, and Michael Winkler. “An Interpolation Inequality Involving LlogL$L\\log L$ Spaces and Application to the Characterization of Blow‐up Behavior in a Two‐dimensional Keller–Segel–Navier–Stokes System.” <i>Journal of the London Mathematical Society</i>, vol. 109, no. 3, e12885, Wiley, 2024, doi:<a href=\"https://doi.org/10.1112/jlms.12885\">10.1112/jlms.12885</a>.","short":"Y. Wang, M. Winkler, Journal of the London Mathematical Society 109 (2024).","apa":"Wang, Y., &#38; Winkler, M. (2024). An interpolation inequality involving LlogL$L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system. <i>Journal of the London Mathematical Society</i>, <i>109</i>(3), Article e12885. <a href=\"https://doi.org/10.1112/jlms.12885\">https://doi.org/10.1112/jlms.12885</a>","chicago":"Wang, Yulan, and Michael Winkler. “An Interpolation Inequality Involving LlogL$L\\log L$ Spaces and Application to the Characterization of Blow‐up Behavior in a Two‐dimensional Keller–Segel–Navier–Stokes System.” <i>Journal of the London Mathematical Society</i> 109, no. 3 (2024). <a href=\"https://doi.org/10.1112/jlms.12885\">https://doi.org/10.1112/jlms.12885</a>.","ieee":"Y. Wang and M. Winkler, “An interpolation inequality involving LlogL$L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system,” <i>Journal of the London Mathematical Society</i>, vol. 109, no. 3, Art. no. e12885, 2024, doi: <a href=\"https://doi.org/10.1112/jlms.12885\">10.1112/jlms.12885</a>.","ama":"Wang Y, Winkler M. An interpolation inequality involving LlogL$L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system. <i>Journal of the London Mathematical Society</i>. 2024;109(3). doi:<a href=\"https://doi.org/10.1112/jlms.12885\">10.1112/jlms.12885</a>"},"intvolume":"       109","year":"2024","issue":"3","publication_status":"published","publication_identifier":{"issn":["0024-6107","1469-7750"]},"language":[{"iso":"eng"}],"article_number":"e12885","user_id":"31496","_id":"63259","status":"public","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>In a smoothly bounded two‐dimensional domain  and for a given nondecreasing positive unbounded , for each  and  the inequality\r\n<jats:disp-formula/>is shown to hold for any positive  fulfilling\r\n<jats:disp-formula/>This is thereafter applied to nonglobal solutions of the Keller–Segel system coupled to the incompressible Navier–Stokes equations through transport and buoyancy, and it is seen that in any such blow‐up event the corresponding population density cannot remain uniformly integrable over  near its explosion time.</jats:p>"}],"type":"journal_article","publication":"Journal of the London Mathematical Society"},{"publication_identifier":{"issn":["0002-9939","1088-6826"]},"publication_status":"published","issue":"10","year":"2024","intvolume":"       152","page":"4325-4341","citation":{"ieee":"Y. Tao and M. Winkler, “Global smooth solutions in a chemotaxis system modeling immune response to a solid tumor,” <i>Proceedings of the American Mathematical Society</i>, vol. 152, no. 10, pp. 4325–4341, 2024, doi: <a href=\"https://doi.org/10.1090/proc/16867\">10.1090/proc/16867</a>.","chicago":"Tao, Youshan, and Michael Winkler. “Global Smooth Solutions in a Chemotaxis System Modeling Immune Response to a Solid Tumor.” <i>Proceedings of the American Mathematical Society</i> 152, no. 10 (2024): 4325–41. <a href=\"https://doi.org/10.1090/proc/16867\">https://doi.org/10.1090/proc/16867</a>.","ama":"Tao Y, Winkler M. Global smooth solutions in a chemotaxis system modeling immune response to a solid tumor. <i>Proceedings of the American Mathematical Society</i>. 2024;152(10):4325-4341. doi:<a href=\"https://doi.org/10.1090/proc/16867\">10.1090/proc/16867</a>","bibtex":"@article{Tao_Winkler_2024, title={Global smooth solutions in a chemotaxis system modeling immune response to a solid tumor}, volume={152}, DOI={<a href=\"https://doi.org/10.1090/proc/16867\">10.1090/proc/16867</a>}, number={10}, journal={Proceedings of the American Mathematical Society}, publisher={American Mathematical Society (AMS)}, author={Tao, Youshan and Winkler, Michael}, year={2024}, pages={4325–4341} }","mla":"Tao, Youshan, and Michael Winkler. “Global Smooth Solutions in a Chemotaxis System Modeling Immune Response to a Solid Tumor.” <i>Proceedings of the American Mathematical Society</i>, vol. 152, no. 10, American Mathematical Society (AMS), 2024, pp. 4325–41, doi:<a href=\"https://doi.org/10.1090/proc/16867\">10.1090/proc/16867</a>.","short":"Y. Tao, M. Winkler, Proceedings of the American Mathematical Society 152 (2024) 4325–4341.","apa":"Tao, Y., &#38; Winkler, M. (2024). Global smooth solutions in a chemotaxis system modeling immune response to a solid tumor. <i>Proceedings of the American Mathematical Society</i>, <i>152</i>(10), 4325–4341. <a href=\"https://doi.org/10.1090/proc/16867\">https://doi.org/10.1090/proc/16867</a>"},"date_updated":"2025-12-18T20:14:30Z","publisher":"American Mathematical Society (AMS)","volume":152,"author":[{"first_name":"Youshan","full_name":"Tao, Youshan","last_name":"Tao"},{"last_name":"Winkler","full_name":"Winkler, Michael","id":"31496","first_name":"Michael"}],"date_created":"2025-12-18T19:07:03Z","title":"Global smooth solutions in a chemotaxis system modeling immune response to a solid tumor","doi":"10.1090/proc/16867","publication":"Proceedings of the American Mathematical Society","type":"journal_article","abstract":[{"lang":"eng","text":"<p>This manuscript studies a no-flux initial-boundary value problem for a four-component chemotaxis system that has been proposed as a model for the response of cytotoxic T-lymphocytes to a solid tumor. In contrast to classical Keller-Segel type situations focusing on two-component interplay of chemotaxing populations with a signal directly secreted by themselves, the presently considered system accounts for a certain indirect mechanism of attractant evolution. Despite the presence of a zero-order exciting nonlinearity of quadratic type that forms a core mathematical feature of the model, the manuscript asserts the global existence of classical solutions for initial data of arbitrary size in three-dimensional domains.</p>"}],"status":"public","_id":"63258","user_id":"31496","language":[{"iso":"eng"}]},{"year":"2024","citation":{"apa":"Nikolić, V., &#38; Winkler, M. (2024). &#60;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si15.svg\" display=\"inline\" id=\"d1e25\"&#62;&#60;mml:msup&#62;&#60;mml:mrow&#62;&#60;mml:mi&#62;L&#60;/mml:mi&#62;&#60;/mml:mrow&#62;&#60;mml:mrow&#62;&#60;mml:mi&#62;∞&#60;/mml:mi&#62;&#60;/mml:mrow&#62;&#60;/mml:msup&#62;&#60;/mml:math&#62; blow-up in the Jordan–Moore–Gibson–Thompson equation. <i>Nonlinear Analysis</i>, <i>247</i>, Article 113600. <a href=\"https://doi.org/10.1016/j.na.2024.113600\">https://doi.org/10.1016/j.na.2024.113600</a>","short":"V. Nikolić, M. Winkler, Nonlinear Analysis 247 (2024).","mla":"Nikolić, Vanja, and Michael Winkler. “&#60;mml:Math Xmlns:Mml=\"http://Www.W3.Org/1998/Math/MathML\" Altimg=\"si15.Svg\" Display=\"inline\" Id=\"d1e25\"&#62;&#60;mml:Msup&#62;&#60;mml:Mrow&#62;&#60;mml:Mi&#62;L&#60;/Mml:Mi&#62;&#60;/Mml:Mrow&#62;&#60;mml:Mrow&#62;&#60;mml:Mi&#62;∞&#60;/Mml:Mi&#62;&#60;/Mml:Mrow&#62;&#60;/Mml:Msup&#62;&#60;/Mml:Math&#62; Blow-up in the Jordan–Moore–Gibson–Thompson Equation.” <i>Nonlinear Analysis</i>, vol. 247, 113600, Elsevier BV, 2024, doi:<a href=\"https://doi.org/10.1016/j.na.2024.113600\">10.1016/j.na.2024.113600</a>.","bibtex":"@article{Nikolić_Winkler_2024, title={&#60;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si15.svg\" display=\"inline\" id=\"d1e25\"&#62;&#60;mml:msup&#62;&#60;mml:mrow&#62;&#60;mml:mi&#62;L&#60;/mml:mi&#62;&#60;/mml:mrow&#62;&#60;mml:mrow&#62;&#60;mml:mi&#62;∞&#60;/mml:mi&#62;&#60;/mml:mrow&#62;&#60;/mml:msup&#62;&#60;/mml:math&#62; blow-up in the Jordan–Moore–Gibson–Thompson equation}, volume={247}, DOI={<a href=\"https://doi.org/10.1016/j.na.2024.113600\">10.1016/j.na.2024.113600</a>}, number={113600}, journal={Nonlinear Analysis}, publisher={Elsevier BV}, author={Nikolić, Vanja and Winkler, Michael}, year={2024} }","ama":"Nikolić V, Winkler M. &#60;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si15.svg\" display=\"inline\" id=\"d1e25\"&#62;&#60;mml:msup&#62;&#60;mml:mrow&#62;&#60;mml:mi&#62;L&#60;/mml:mi&#62;&#60;/mml:mrow&#62;&#60;mml:mrow&#62;&#60;mml:mi&#62;∞&#60;/mml:mi&#62;&#60;/mml:mrow&#62;&#60;/mml:msup&#62;&#60;/mml:math&#62; blow-up in the Jordan–Moore–Gibson–Thompson equation. <i>Nonlinear Analysis</i>. 2024;247. doi:<a href=\"https://doi.org/10.1016/j.na.2024.113600\">10.1016/j.na.2024.113600</a>","chicago":"Nikolić, Vanja, and Michael Winkler. “&#60;mml:Math Xmlns:Mml=\"http://Www.W3.Org/1998/Math/MathML\" Altimg=\"si15.Svg\" Display=\"inline\" Id=\"d1e25\"&#62;&#60;mml:Msup&#62;&#60;mml:Mrow&#62;&#60;mml:Mi&#62;L&#60;/Mml:Mi&#62;&#60;/Mml:Mrow&#62;&#60;mml:Mrow&#62;&#60;mml:Mi&#62;∞&#60;/Mml:Mi&#62;&#60;/Mml:Mrow&#62;&#60;/Mml:Msup&#62;&#60;/Mml:Math&#62; Blow-up in the Jordan–Moore–Gibson–Thompson Equation.” <i>Nonlinear Analysis</i> 247 (2024). <a href=\"https://doi.org/10.1016/j.na.2024.113600\">https://doi.org/10.1016/j.na.2024.113600</a>.","ieee":"V. Nikolić and M. Winkler, “&#60;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si15.svg\" display=\"inline\" id=\"d1e25\"&#62;&#60;mml:msup&#62;&#60;mml:mrow&#62;&#60;mml:mi&#62;L&#60;/mml:mi&#62;&#60;/mml:mrow&#62;&#60;mml:mrow&#62;&#60;mml:mi&#62;∞&#60;/mml:mi&#62;&#60;/mml:mrow&#62;&#60;/mml:msup&#62;&#60;/mml:math&#62; blow-up in the Jordan–Moore–Gibson–Thompson equation,” <i>Nonlinear Analysis</i>, vol. 247, Art. no. 113600, 2024, doi: <a href=\"https://doi.org/10.1016/j.na.2024.113600\">10.1016/j.na.2024.113600</a>."},"intvolume":"       247","publication_status":"published","publication_identifier":{"issn":["0362-546X"]},"title":"<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si15.svg\" display=\"inline\" id=\"d1e25\"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msup></mml:math> blow-up in the Jordan–Moore–Gibson–Thompson equation","doi":"10.1016/j.na.2024.113600","date_updated":"2025-12-18T20:14:12Z","publisher":"Elsevier BV","author":[{"last_name":"Nikolić","full_name":"Nikolić, Vanja","first_name":"Vanja"},{"last_name":"Winkler","id":"31496","full_name":"Winkler, Michael","first_name":"Michael"}],"date_created":"2025-12-18T19:06:09Z","volume":247,"status":"public","type":"journal_article","publication":"Nonlinear Analysis","article_number":"113600","language":[{"iso":"eng"}],"_id":"63256","user_id":"31496"},{"title":"A singular growth phenomenon in a Keller–Segel–type parabolic system involving density‐suppressed motilities","doi":"10.1002/mana.202300361","date_updated":"2025-12-18T20:14:46Z","publisher":"Wiley","volume":297,"date_created":"2025-12-18T19:07:48Z","author":[{"first_name":"Yulan","last_name":"Wang","full_name":"Wang, Yulan"},{"first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael","id":"31496"}],"year":"2024","page":"2353-2364","intvolume":"       297","citation":{"apa":"Wang, Y., &#38; Winkler, M. (2024). A singular growth phenomenon in a Keller–Segel–type parabolic system involving density‐suppressed motilities. <i>Mathematische Nachrichten</i>, <i>297</i>(6), 2353–2364. <a href=\"https://doi.org/10.1002/mana.202300361\">https://doi.org/10.1002/mana.202300361</a>","short":"Y. Wang, M. Winkler, Mathematische Nachrichten 297 (2024) 2353–2364.","bibtex":"@article{Wang_Winkler_2024, title={A singular growth phenomenon in a Keller–Segel–type parabolic system involving density‐suppressed motilities}, volume={297}, DOI={<a href=\"https://doi.org/10.1002/mana.202300361\">10.1002/mana.202300361</a>}, number={6}, journal={Mathematische Nachrichten}, publisher={Wiley}, author={Wang, Yulan and Winkler, Michael}, year={2024}, pages={2353–2364} }","mla":"Wang, Yulan, and Michael Winkler. “A Singular Growth Phenomenon in a Keller–Segel–Type Parabolic System Involving Density‐suppressed Motilities.” <i>Mathematische Nachrichten</i>, vol. 297, no. 6, Wiley, 2024, pp. 2353–64, doi:<a href=\"https://doi.org/10.1002/mana.202300361\">10.1002/mana.202300361</a>.","ama":"Wang Y, Winkler M. A singular growth phenomenon in a Keller–Segel–type parabolic system involving density‐suppressed motilities. <i>Mathematische Nachrichten</i>. 2024;297(6):2353-2364. doi:<a href=\"https://doi.org/10.1002/mana.202300361\">10.1002/mana.202300361</a>","ieee":"Y. Wang and M. Winkler, “A singular growth phenomenon in a Keller–Segel–type parabolic system involving density‐suppressed motilities,” <i>Mathematische Nachrichten</i>, vol. 297, no. 6, pp. 2353–2364, 2024, doi: <a href=\"https://doi.org/10.1002/mana.202300361\">10.1002/mana.202300361</a>.","chicago":"Wang, Yulan, and Michael Winkler. “A Singular Growth Phenomenon in a Keller–Segel–Type Parabolic System Involving Density‐suppressed Motilities.” <i>Mathematische Nachrichten</i> 297, no. 6 (2024): 2353–64. <a href=\"https://doi.org/10.1002/mana.202300361\">https://doi.org/10.1002/mana.202300361</a>."},"publication_identifier":{"issn":["0025-584X","1522-2616"]},"publication_status":"published","issue":"6","language":[{"iso":"eng"}],"_id":"63260","user_id":"31496","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>A no‐flux initial‐boundary value problem for\r\n<jats:disp-formula/>is considered in a ball , where  and .</jats:p><jats:p>Under the assumption that , it is shown that for each , there exist  and a positive  with the property that whenever  is nonnegative with , the global solutions to () emanating from the initial data  have the property that\r\n<jats:disp-formula/></jats:p>","lang":"eng"}],"status":"public","publication":"Mathematische Nachrichten","type":"journal_article"},{"intvolume":"       263","page":"93-127","citation":{"short":"M. Winkler, Israel Journal of Mathematics 263 (2024) 93–127.","bibtex":"@article{Winkler_2024, title={Complete infinite-time mass aggregation in a quasilinear Keller–Segel system}, volume={263}, DOI={<a href=\"https://doi.org/10.1007/s11856-024-2618-9\">10.1007/s11856-024-2618-9</a>}, number={1}, journal={Israel Journal of Mathematics}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2024}, pages={93–127} }","mla":"Winkler, Michael. “Complete Infinite-Time Mass Aggregation in a Quasilinear Keller–Segel System.” <i>Israel Journal of Mathematics</i>, vol. 263, no. 1, Springer Science and Business Media LLC, 2024, pp. 93–127, doi:<a href=\"https://doi.org/10.1007/s11856-024-2618-9\">10.1007/s11856-024-2618-9</a>.","apa":"Winkler, M. (2024). Complete infinite-time mass aggregation in a quasilinear Keller–Segel system. <i>Israel Journal of Mathematics</i>, <i>263</i>(1), 93–127. <a href=\"https://doi.org/10.1007/s11856-024-2618-9\">https://doi.org/10.1007/s11856-024-2618-9</a>","ama":"Winkler M. Complete infinite-time mass aggregation in a quasilinear Keller–Segel system. <i>Israel Journal of Mathematics</i>. 2024;263(1):93-127. doi:<a href=\"https://doi.org/10.1007/s11856-024-2618-9\">10.1007/s11856-024-2618-9</a>","chicago":"Winkler, Michael. “Complete Infinite-Time Mass Aggregation in a Quasilinear Keller–Segel System.” <i>Israel Journal of Mathematics</i> 263, no. 1 (2024): 93–127. <a href=\"https://doi.org/10.1007/s11856-024-2618-9\">https://doi.org/10.1007/s11856-024-2618-9</a>.","ieee":"M. Winkler, “Complete infinite-time mass aggregation in a quasilinear Keller–Segel system,” <i>Israel Journal of Mathematics</i>, vol. 263, no. 1, pp. 93–127, 2024, doi: <a href=\"https://doi.org/10.1007/s11856-024-2618-9\">10.1007/s11856-024-2618-9</a>."},"year":"2024","issue":"1","publication_identifier":{"issn":["0021-2172","1565-8511"]},"publication_status":"published","doi":"10.1007/s11856-024-2618-9","title":"Complete infinite-time mass aggregation in a quasilinear Keller–Segel system","volume":263,"author":[{"first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael","id":"31496"}],"date_created":"2025-12-18T19:08:34Z","date_updated":"2025-12-18T20:14:59Z","publisher":"Springer Science and Business Media LLC","status":"public","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>Radially symmetric global unbounded solutions of the chemotaxis system <jats:disp-formula><jats:alternatives><jats:tex-math>$$\\left\\{ {\\matrix{{{u_t} = \\nabla \\cdot (D(u)\\nabla u) - \\nabla \\cdot (uS(u)\\nabla v),} \\hfill &amp; {} \\hfill \\cr {0 = \\Delta v - \\mu + u,} \\hfill &amp; {\\mu = {1 \\over {|\\Omega |}}\\int_\\Omega {u,} } \\hfill \\cr } } \\right.$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mrow>\r\n                      <mml:mo>{</mml:mo>\r\n                      <mml:mrow>\r\n                        <mml:mtable>\r\n                          <mml:mtr>\r\n                            <mml:mtd>\r\n                              <mml:mrow>\r\n                                <mml:msub>\r\n                                  <mml:mi>u</mml:mi>\r\n                                  <mml:mi>t</mml:mi>\r\n                                </mml:msub>\r\n                                <mml:mo>=</mml:mo>\r\n                                <mml:mo>∇</mml:mo>\r\n                                <mml:mo>⋅</mml:mo>\r\n                                <mml:mo>(</mml:mo>\r\n                                <mml:mi>D</mml:mi>\r\n                                <mml:mo>(</mml:mo>\r\n                                <mml:mi>u</mml:mi>\r\n                                <mml:mo>)</mml:mo>\r\n                                <mml:mo>∇</mml:mo>\r\n                                <mml:mi>u</mml:mi>\r\n                                <mml:mo>)</mml:mo>\r\n                                <mml:mo>−</mml:mo>\r\n                                <mml:mo>∇</mml:mo>\r\n                                <mml:mo>⋅</mml:mo>\r\n                                <mml:mo>(</mml:mo>\r\n                                <mml:mi>u</mml:mi>\r\n                                <mml:mi>S</mml:mi>\r\n                                <mml:mo>(</mml:mo>\r\n                                <mml:mi>u</mml:mi>\r\n                                <mml:mo>)</mml:mo>\r\n                                <mml:mo>∇</mml:mo>\r\n                                <mml:mi>v</mml:mi>\r\n                                <mml:mo>)</mml:mo>\r\n                                <mml:mo>,</mml:mo>\r\n                              </mml:mrow>\r\n                            </mml:mtd>\r\n                            <mml:mtd>\r\n                              <mml:mrow/>\r\n                            </mml:mtd>\r\n                          </mml:mtr>\r\n                          <mml:mtr>\r\n                            <mml:mtd>\r\n                              <mml:mrow>\r\n                                <mml:mn>0</mml:mn>\r\n                                <mml:mo>=</mml:mo>\r\n                                <mml:mi>Δ</mml:mi>\r\n                                <mml:mi>v</mml:mi>\r\n                                <mml:mo>−</mml:mo>\r\n                                <mml:mi>μ</mml:mi>\r\n                                <mml:mo>+</mml:mo>\r\n                                <mml:mi>u</mml:mi>\r\n                                <mml:mo>,</mml:mo>\r\n                              </mml:mrow>\r\n                            </mml:mtd>\r\n                            <mml:mtd>\r\n                              <mml:mrow>\r\n                                <mml:mi>μ</mml:mi>\r\n                                <mml:mo>=</mml:mo>\r\n                                <mml:mfrac>\r\n                                  <mml:mn>1</mml:mn>\r\n                                  <mml:mrow>\r\n                                    <mml:mo>|</mml:mo>\r\n                                    <mml:mi>Ω</mml:mi>\r\n                                    <mml:mo>|</mml:mo>\r\n                                  </mml:mrow>\r\n                                </mml:mfrac>\r\n                                <mml:mstyle>\r\n                                  <mml:mrow>\r\n                                    <mml:msub>\r\n                                      <mml:mo>∫</mml:mo>\r\n                                      <mml:mi>Ω</mml:mi>\r\n                                    </mml:msub>\r\n                                    <mml:mrow>\r\n                                      <mml:mi>u</mml:mi>\r\n                                      <mml:mo>,</mml:mo>\r\n                                    </mml:mrow>\r\n                                  </mml:mrow>\r\n                                </mml:mstyle>\r\n                              </mml:mrow>\r\n                            </mml:mtd>\r\n                          </mml:mtr>\r\n                        </mml:mtable>\r\n                      </mml:mrow>\r\n                    </mml:mrow>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:disp-formula> are considered in a ball Ω = <jats:italic>B</jats:italic><jats:sub><jats:italic>R</jats:italic></jats:sub>(0) ⊂ ℝ<jats:sup><jats:italic>n</jats:italic></jats:sup>, where <jats:italic>n</jats:italic> ≥ 3 and <jats:italic>R</jats:italic> &gt; 0.</jats:p><jats:p>Under the assumption that <jats:italic>D</jats:italic> and <jats:italic>S</jats:italic> suitably generalize the prototypes given by <jats:italic>D</jats:italic>(<jats:italic>ξ</jats:italic>) = (<jats:italic>ξ</jats:italic> + <jats:italic>ι</jats:italic>)<jats:sup>m−1</jats:sup> and <jats:italic>S</jats:italic>(<jats:italic>ξ</jats:italic>) = (<jats:italic>ξ</jats:italic> + 1)<jats:sup>−λ−1</jats:sup> for all <jats:italic>ξ</jats:italic> &gt; 0 and some <jats:italic>m</jats:italic> ∈ ℝ, λ &gt;0 and <jats:italic>ι</jats:italic> ≥ 0 fulfilling <jats:inline-formula><jats:alternatives><jats:tex-math>$$m + \\lambda &lt; 1 - {2 \\over n}$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mi>m</mml:mi>\r\n                  <mml:mo>+</mml:mo>\r\n                  <mml:mi>λ</mml:mi>\r\n                  <mml:mo>&lt;</mml:mo>\r\n                  <mml:mn>1</mml:mn>\r\n                  <mml:mo>−</mml:mo>\r\n                  <mml:mfrac>\r\n                    <mml:mn>2</mml:mn>\r\n                    <mml:mi>n</mml:mi>\r\n                  </mml:mfrac>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, a considerably large set of initial data <jats:italic>u</jats:italic><jats:sub>0</jats:sub> is found to enforce a complete mass aggregation in infinite time in the sense that for any such <jats:italic>u</jats:italic><jats:sub>0</jats:sub>, an associated Neumann type initial-boundary value problem admits a global classical solution (<jats:italic>u, v</jats:italic>) satisfying <jats:disp-formula><jats:alternatives><jats:tex-math>$${1 \\over C} \\cdot {(t + 1)^{{1 \\over \\lambda }}} \\le ||u( \\cdot ,t)|{|_{{L^\\infty }(\\Omega )}} \\le C \\cdot {(t + 1)^{{1 \\over \\lambda }}}\\,\\,\\,{\\rm{for}}\\,\\,{\\rm{all}}\\,\\,t &gt; 0$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mfrac>\r\n                      <mml:mn>1</mml:mn>\r\n                      <mml:mi>C</mml:mi>\r\n                    </mml:mfrac>\r\n                  </mml:mrow>\r\n                  <mml:mo>⋅</mml:mo>\r\n                  <mml:mrow>\r\n                    <mml:mo>(</mml:mo>\r\n                    <mml:mi>t</mml:mi>\r\n                    <mml:mo>+</mml:mo>\r\n                    <mml:mn>1</mml:mn>\r\n                    <mml:msup>\r\n                      <mml:mo>)</mml:mo>\r\n                      <mml:mrow>\r\n                        <mml:mrow>\r\n                          <mml:mfrac>\r\n                            <mml:mn>1</mml:mn>\r\n                            <mml:mi>λ</mml:mi>\r\n                          </mml:mfrac>\r\n                        </mml:mrow>\r\n                      </mml:mrow>\r\n                    </mml:msup>\r\n                  </mml:mrow>\r\n                  <mml:mo>≤</mml:mo>\r\n                  <mml:mrow>\r\n                    <mml:mo>|</mml:mo>\r\n                  </mml:mrow>\r\n                  <mml:mrow>\r\n                    <mml:mo>|</mml:mo>\r\n                  </mml:mrow>\r\n                  <mml:mi>u</mml:mi>\r\n                  <mml:mo>(</mml:mo>\r\n                  <mml:mo>⋅</mml:mo>\r\n                  <mml:mo>,</mml:mo>\r\n                  <mml:mi>t</mml:mi>\r\n                  <mml:mo>)</mml:mo>\r\n                  <mml:mrow>\r\n                    <mml:mo>|</mml:mo>\r\n                  </mml:mrow>\r\n                  <mml:mrow>\r\n                    <mml:msub>\r\n                      <mml:mrow>\r\n                        <mml:mo>|</mml:mo>\r\n                      </mml:mrow>\r\n                      <mml:mrow>\r\n                        <mml:mrow>\r\n                          <mml:msup>\r\n                            <mml:mi>L</mml:mi>\r\n                            <mml:mi>∞</mml:mi>\r\n                          </mml:msup>\r\n                        </mml:mrow>\r\n                        <mml:mo>(</mml:mo>\r\n                        <mml:mi>Ω</mml:mi>\r\n                        <mml:mo>)</mml:mo>\r\n                      </mml:mrow>\r\n                    </mml:msub>\r\n                  </mml:mrow>\r\n                  <mml:mo>≤</mml:mo>\r\n                  <mml:mi>C</mml:mi>\r\n                  <mml:mo>⋅</mml:mo>\r\n                  <mml:mrow>\r\n                    <mml:mo>(</mml:mo>\r\n                    <mml:mi>t</mml:mi>\r\n                    <mml:mo>+</mml:mo>\r\n                    <mml:mn>1</mml:mn>\r\n                    <mml:msup>\r\n                      <mml:mo>)</mml:mo>\r\n                      <mml:mrow>\r\n                        <mml:mrow>\r\n                          <mml:mfrac>\r\n                            <mml:mn>1</mml:mn>\r\n                            <mml:mi>λ</mml:mi>\r\n                          </mml:mfrac>\r\n                        </mml:mrow>\r\n                      </mml:mrow>\r\n                    </mml:msup>\r\n                  </mml:mrow>\r\n                  <mml:mspace/>\r\n                  <mml:mspace/>\r\n                  <mml:mspace/>\r\n                  <mml:mrow>\r\n                    <mml:mrow>\r\n                      <mml:mi>f</mml:mi>\r\n                      <mml:mi>o</mml:mi>\r\n                      <mml:mi>r</mml:mi>\r\n                    </mml:mrow>\r\n                  </mml:mrow>\r\n                  <mml:mspace/>\r\n                  <mml:mspace/>\r\n                  <mml:mrow>\r\n                    <mml:mrow>\r\n                      <mml:mi>a</mml:mi>\r\n                      <mml:mi>l</mml:mi>\r\n                      <mml:mi>l</mml:mi>\r\n                    </mml:mrow>\r\n                  </mml:mrow>\r\n                  <mml:mspace/>\r\n                  <mml:mspace/>\r\n                  <mml:mi>t</mml:mi>\r\n                  <mml:mo>&gt;</mml:mo>\r\n                  <mml:mn>0</mml:mn>\r\n                </mml:math></jats:alternatives></jats:disp-formula> as well as <jats:disp-formula><jats:alternatives><jats:tex-math>$$||u( \\cdot \\,,t)|{|_{{L^1}(\\Omega \\backslash {B_{{r_0}}}(0))}} \\to 0\\,\\,\\,{\\rm{as}}\\,\\,t \\to \\infty \\,\\,\\,{\\rm{for}}\\,\\,{\\rm{all}}\\,\\,{r_0} \\in (0,R)$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mo>|</mml:mo>\r\n                  <mml:mo>|</mml:mo>\r\n                  <mml:mi>u</mml:mi>\r\n                  <mml:mo>(</mml:mo>\r\n                  <mml:mo>⋅</mml:mo>\r\n                  <mml:mo>,</mml:mo>\r\n                  <mml:mi>t</mml:mi>\r\n                  <mml:mo>)</mml:mo>\r\n                  <mml:mo>|</mml:mo>\r\n                  <mml:msub>\r\n                    <mml:mo>|</mml:mo>\r\n                    <mml:mrow>\r\n                      <mml:msup>\r\n                        <mml:mi>L</mml:mi>\r\n                        <mml:mn>1</mml:mn>\r\n                      </mml:msup>\r\n                      <mml:mo>(</mml:mo>\r\n                      <mml:mi>Ω</mml:mi>\r\n                      <mml:mo>\\</mml:mo>\r\n                      <mml:msub>\r\n                        <mml:mi>B</mml:mi>\r\n                        <mml:mrow>\r\n                          <mml:msub>\r\n                            <mml:mi>r</mml:mi>\r\n                            <mml:mn>0</mml:mn>\r\n                          </mml:msub>\r\n                        </mml:mrow>\r\n                      </mml:msub>\r\n                      <mml:mo>(</mml:mo>\r\n                      <mml:mn>0</mml:mn>\r\n                      <mml:mo>)</mml:mo>\r\n                      <mml:mo>)</mml:mo>\r\n                    </mml:mrow>\r\n                  </mml:msub>\r\n                  <mml:mo>→</mml:mo>\r\n                  <mml:mn>0</mml:mn>\r\n                  <mml:mtext>as</mml:mtext>\r\n                  <mml:mi>t</mml:mi>\r\n                  <mml:mo>→</mml:mo>\r\n                  <mml:mi>∞</mml:mi>\r\n                  <mml:mtext>for all</mml:mtext>\r\n                  <mml:msub>\r\n                    <mml:mi>r</mml:mi>\r\n                    <mml:mn>0</mml:mn>\r\n                  </mml:msub>\r\n                  <mml:mo>∈</mml:mo>\r\n                  <mml:mo>(</mml:mo>\r\n                  <mml:mn>0</mml:mn>\r\n                  <mml:mo>,</mml:mo>\r\n                  <mml:mi>R</mml:mi>\r\n                  <mml:mo>)</mml:mo>\r\n                </mml:math></jats:alternatives></jats:disp-formula> with some <jats:italic>C</jats:italic> &gt; 0.</jats:p>"}],"publication":"Israel Journal of Mathematics","type":"journal_article","language":[{"iso":"eng"}],"user_id":"31496","_id":"63262"},{"publication":"Journal of Differential Equations","type":"journal_article","status":"public","user_id":"31496","_id":"63263","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0022-0396"]},"publication_status":"published","page":"423-456","intvolume":"       400","citation":{"bibtex":"@article{Winkler_2024, title={L∞ bounds in a two-dimensional doubly degenerate nutrient taxis system with general cross-diffusive flux}, volume={400}, DOI={<a href=\"https://doi.org/10.1016/j.jde.2024.04.028\">10.1016/j.jde.2024.04.028</a>}, journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Winkler, Michael}, year={2024}, pages={423–456} }","short":"M. Winkler, Journal of Differential Equations 400 (2024) 423–456.","mla":"Winkler, Michael. “L∞ Bounds in a Two-Dimensional Doubly Degenerate Nutrient Taxis System with General Cross-Diffusive Flux.” <i>Journal of Differential Equations</i>, vol. 400, Elsevier BV, 2024, pp. 423–56, doi:<a href=\"https://doi.org/10.1016/j.jde.2024.04.028\">10.1016/j.jde.2024.04.028</a>.","apa":"Winkler, M. (2024). L∞ bounds in a two-dimensional doubly degenerate nutrient taxis system with general cross-diffusive flux. <i>Journal of Differential Equations</i>, <i>400</i>, 423–456. <a href=\"https://doi.org/10.1016/j.jde.2024.04.028\">https://doi.org/10.1016/j.jde.2024.04.028</a>","ama":"Winkler M. L∞ bounds in a two-dimensional doubly degenerate nutrient taxis system with general cross-diffusive flux. <i>Journal of Differential Equations</i>. 2024;400:423-456. doi:<a href=\"https://doi.org/10.1016/j.jde.2024.04.028\">10.1016/j.jde.2024.04.028</a>","ieee":"M. Winkler, “L∞ bounds in a two-dimensional doubly degenerate nutrient taxis system with general cross-diffusive flux,” <i>Journal of Differential Equations</i>, vol. 400, pp. 423–456, 2024, doi: <a href=\"https://doi.org/10.1016/j.jde.2024.04.028\">10.1016/j.jde.2024.04.028</a>.","chicago":"Winkler, Michael. “L∞ Bounds in a Two-Dimensional Doubly Degenerate Nutrient Taxis System with General Cross-Diffusive Flux.” <i>Journal of Differential Equations</i> 400 (2024): 423–56. <a href=\"https://doi.org/10.1016/j.jde.2024.04.028\">https://doi.org/10.1016/j.jde.2024.04.028</a>."},"year":"2024","volume":400,"author":[{"last_name":"Winkler","full_name":"Winkler, Michael","id":"31496","first_name":"Michael"}],"date_created":"2025-12-18T19:09:07Z","publisher":"Elsevier BV","date_updated":"2025-12-18T20:15:05Z","doi":"10.1016/j.jde.2024.04.028","title":"L∞ bounds in a two-dimensional doubly degenerate nutrient taxis system with general cross-diffusive flux"},{"article_type":"original","article_number":"23945","_id":"54815","user_id":"78890","department":[{"_id":"15"},{"_id":"623"},{"_id":"288"}],"status":"public","type":"journal_article","doi":"10.1364/oe.522549","date_updated":"2025-12-19T11:37:41Z","author":[{"first_name":"René","last_name":"Pollmann","full_name":"Pollmann, René","id":"78890"},{"full_name":"Roeder, Franz","id":"88149","last_name":"Roeder","first_name":"Franz"},{"last_name":"Quiring","full_name":"Quiring, Victor","first_name":"Victor"},{"first_name":"Raimund","full_name":"Ricken, Raimund","last_name":"Ricken"},{"first_name":"Christof","orcid":"https://orcid.org/0000-0002-5693-3083","last_name":"Eigner","full_name":"Eigner, Christof","id":"13244"},{"first_name":"Benjamin","last_name":"Brecht","orcid":"0000-0003-4140-0556 ","id":"27150","full_name":"Brecht, Benjamin"},{"first_name":"Christine","last_name":"Silberhorn","full_name":"Silberhorn, Christine","id":"26263"}],"volume":32,"citation":{"apa":"Pollmann, R., Roeder, F., Quiring, V., Ricken, R., Eigner, C., Brecht, B., &#38; Silberhorn, C. (2024). Integrated, bright broadband, two-colour parametric down-conversion source. <i>Optics Express</i>, <i>32</i>(14), Article 23945. <a href=\"https://doi.org/10.1364/oe.522549\">https://doi.org/10.1364/oe.522549</a>","mla":"Pollmann, René, et al. “Integrated, Bright Broadband, Two-Colour Parametric down-Conversion Source.” <i>Optics Express</i>, vol. 32, no. 14, 23945, Optica Publishing Group, 2024, doi:<a href=\"https://doi.org/10.1364/oe.522549\">10.1364/oe.522549</a>.","bibtex":"@article{Pollmann_Roeder_Quiring_Ricken_Eigner_Brecht_Silberhorn_2024, title={Integrated, bright broadband, two-colour parametric down-conversion source}, volume={32}, DOI={<a href=\"https://doi.org/10.1364/oe.522549\">10.1364/oe.522549</a>}, number={1423945}, journal={Optics Express}, publisher={Optica Publishing Group}, author={Pollmann, René and Roeder, Franz and Quiring, Victor and Ricken, Raimund and Eigner, Christof and Brecht, Benjamin and Silberhorn, Christine}, year={2024} }","short":"R. Pollmann, F. Roeder, V. Quiring, R. Ricken, C. Eigner, B. Brecht, C. Silberhorn, Optics Express 32 (2024).","ieee":"R. Pollmann <i>et al.</i>, “Integrated, bright broadband, two-colour parametric down-conversion source,” <i>Optics Express</i>, vol. 32, no. 14, Art. no. 23945, 2024, doi: <a href=\"https://doi.org/10.1364/oe.522549\">10.1364/oe.522549</a>.","chicago":"Pollmann, René, Franz Roeder, Victor Quiring, Raimund Ricken, Christof Eigner, Benjamin Brecht, and Christine Silberhorn. “Integrated, Bright Broadband, Two-Colour Parametric down-Conversion Source.” <i>Optics Express</i> 32, no. 14 (2024). <a href=\"https://doi.org/10.1364/oe.522549\">https://doi.org/10.1364/oe.522549</a>.","ama":"Pollmann R, Roeder F, Quiring V, et al. Integrated, bright broadband, two-colour parametric down-conversion source. <i>Optics Express</i>. 2024;32(14). doi:<a href=\"https://doi.org/10.1364/oe.522549\">10.1364/oe.522549</a>"},"intvolume":"        32","publication_status":"published","publication_identifier":{"issn":["1094-4087"]},"language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"<jats:p>Broadband quantum light is a vital resource for quantum metrology and spectroscopy applications such as quantum optical coherence tomography or entangled two photon absorption. For entangled two photon absorption in particular, very high photon flux combined with high time-frequency entanglement is crucial for observing a signal. So far these conditions could be met by using high power lasers driving degenerate, type 0 bulk-crystal spontaneous parametric down conversion (SPDC) sources. This naturally limits the available wavelength ranges and precludes deterministic splitting of the generated output photons. In this work we demonstrate an integrated two-colour SPDC source utilising a group-velocity matched lithium niobate waveguide, reaching both exceptional brightness 1.52⋅10<jats:sup>6</jats:sup>pairssmWGHz and large bandwidth (7.8 THz FWHM) while pumped with a few mW of continuous wave (CW) laser light. By converting a narrow band pump to broadband pulses the created photon pairs show correlation times of Δ<jats:italic>τ</jats:italic> ≈ 120 fs while maintaining the narrow bandwidth Δ<jats:italic>ω</jats:italic><jats:sub>\r\n      <jats:italic>p</jats:italic>\r\n    </jats:sub> ≪ 1 MHz of the CW pump light, yielding strong time-frequency entanglement. Furthermore our process can be adapted to a wide range of central wavelengths.</jats:p>"}],"publication":"Optics Express","title":"Integrated, bright broadband, two-colour parametric down-conversion source","publisher":"Optica Publishing Group","date_created":"2024-06-19T06:58:17Z","year":"2024","issue":"14"},{"_id":"57862","project":[{"_id":"571","name":"MIRAQLS: MIRAQLS: Mid-infrared Quantum Technology for Sensing"},{"_id":"190","name":"E2TPA: Exploiting Entangled Two-Photon Absorption"}],"department":[{"_id":"288"},{"_id":"623"},{"_id":"15"}],"user_id":"78890","article_type":"original","article_number":"123025","language":[{"iso":"eng"}],"publication":"New Journal of Physics","type":"journal_article","abstract":[{"text":"The latest applications in ultrafast quantum metrology require bright, broadband bi-photon sources with one of the photons in the mid-infrared and the other in the visible to near infrared. However, existing sources based on bulk crystals are limited in brightness due to the short interaction length and only allow for limited dispersion engineering. Here, we present an integrated PDC source based on a Ti:LiNbO3 waveguide that generates broadband bi-photons with central wavelengths at 860 nm and 2800 nm. Their spectral bandwidth exceeds 25 THz and is achieved by simultaneous matching of the group velocities (GVs) and cancellation of GV dispersion for the signal and idler field. We provide an intuitive understanding of the process by studying our source’s behavior at different temperatures and pump wavelengths, which agrees well with simulations.","lang":"eng"}],"status":"public","date_updated":"2025-12-19T11:36:36Z","publisher":"IOP Publishing","volume":26,"author":[{"first_name":"Franz","full_name":"Roeder, Franz","id":"88149","last_name":"Roeder"},{"first_name":"Abira","last_name":"Gnanavel","full_name":"Gnanavel, Abira"},{"first_name":"René","full_name":"Pollmann, René","id":"78890","last_name":"Pollmann"},{"full_name":"Brecht, Olga","last_name":"Brecht","first_name":"Olga"},{"first_name":"Michael","id":"42777","full_name":"Stefszky, Michael","last_name":"Stefszky"},{"id":"40300","full_name":"Padberg, Laura","last_name":"Padberg","first_name":"Laura"},{"first_name":"Christof","full_name":"Eigner, Christof","id":"13244","orcid":"https://orcid.org/0000-0002-5693-3083","last_name":"Eigner"},{"id":"26263","full_name":"Silberhorn, Christine","last_name":"Silberhorn","first_name":"Christine"},{"first_name":"Benjamin","orcid":"0000-0003-4140-0556 ","last_name":"Brecht","id":"27150","full_name":"Brecht, Benjamin"}],"date_created":"2024-12-27T19:01:14Z","title":"Ultra-broadband non-degenerate guided-wave bi-photon source in the near and mid-infrared","doi":"10.1088/1367-2630/ad9f98","publication_identifier":{"issn":["1367-2630"]},"publication_status":"published","issue":"12","year":"2024","intvolume":"        26","citation":{"mla":"Roeder, Franz, et al. “Ultra-Broadband Non-Degenerate Guided-Wave Bi-Photon Source in the near and Mid-Infrared.” <i>New Journal of Physics</i>, vol. 26, no. 12, 123025, IOP Publishing, 2024, doi:<a href=\"https://doi.org/10.1088/1367-2630/ad9f98\">10.1088/1367-2630/ad9f98</a>.","short":"F. Roeder, A. Gnanavel, R. Pollmann, O. Brecht, M. Stefszky, L. Padberg, C. Eigner, C. Silberhorn, B. Brecht, New Journal of Physics 26 (2024).","bibtex":"@article{Roeder_Gnanavel_Pollmann_Brecht_Stefszky_Padberg_Eigner_Silberhorn_Brecht_2024, title={Ultra-broadband non-degenerate guided-wave bi-photon source in the near and mid-infrared}, volume={26}, DOI={<a href=\"https://doi.org/10.1088/1367-2630/ad9f98\">10.1088/1367-2630/ad9f98</a>}, number={12123025}, journal={New Journal of Physics}, publisher={IOP Publishing}, author={Roeder, Franz and Gnanavel, Abira and Pollmann, René and Brecht, Olga and Stefszky, Michael and Padberg, Laura and Eigner, Christof and Silberhorn, Christine and Brecht, Benjamin}, year={2024} }","apa":"Roeder, F., Gnanavel, A., Pollmann, R., Brecht, O., Stefszky, M., Padberg, L., Eigner, C., Silberhorn, C., &#38; Brecht, B. (2024). Ultra-broadband non-degenerate guided-wave bi-photon source in the near and mid-infrared. <i>New Journal of Physics</i>, <i>26</i>(12), Article 123025. <a href=\"https://doi.org/10.1088/1367-2630/ad9f98\">https://doi.org/10.1088/1367-2630/ad9f98</a>","ama":"Roeder F, Gnanavel A, Pollmann R, et al. Ultra-broadband non-degenerate guided-wave bi-photon source in the near and mid-infrared. <i>New Journal of Physics</i>. 2024;26(12). doi:<a href=\"https://doi.org/10.1088/1367-2630/ad9f98\">10.1088/1367-2630/ad9f98</a>","chicago":"Roeder, Franz, Abira Gnanavel, René Pollmann, Olga Brecht, Michael Stefszky, Laura Padberg, Christof Eigner, Christine Silberhorn, and Benjamin Brecht. “Ultra-Broadband Non-Degenerate Guided-Wave Bi-Photon Source in the near and Mid-Infrared.” <i>New Journal of Physics</i> 26, no. 12 (2024). <a href=\"https://doi.org/10.1088/1367-2630/ad9f98\">https://doi.org/10.1088/1367-2630/ad9f98</a>.","ieee":"F. Roeder <i>et al.</i>, “Ultra-broadband non-degenerate guided-wave bi-photon source in the near and mid-infrared,” <i>New Journal of Physics</i>, vol. 26, no. 12, Art. no. 123025, 2024, doi: <a href=\"https://doi.org/10.1088/1367-2630/ad9f98\">10.1088/1367-2630/ad9f98</a>."}},{"language":[{"iso":"eng"}],"publication":"Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications","abstract":[{"lang":"eng","text":"<jats:p> Lightweight design by using low-density and load-adapted materials can reduce the weight of vehicles and the emissions generated during operation. However, the usage of different materials requires innovative joining technologies with increased versatility. In this investigation, the focus is on describing and characterising the failure behaviour of connections manufactured by an innovative thermomechanical joining process with adaptable auxiliary joining elements in single-lap tensile-shear tests. In order to analyse the failure development in detail, the specimens are investigated using in-situ computed tomography (in-situ CT). Here, the tensile-shear test is interrupted at points of interest and CT scans are conducted under load. In addition, the interrupted in-situ testing procedure is validated by comparing the loading behaviour with conventional continuous tensile-shear tests. The results of the in-situ investigations of joints with varying material combinations clearly describe the cause of failure, allowing conclusions towards an improved joint design. </jats:p>"}],"publisher":"SAGE Publications","date_created":"2025-12-19T09:13:30Z","title":"In-situ computed tomography analysis of the failure mechanisms of thermomechanically manufactured joints with auxiliary joining element","quality_controlled":"1","issue":"12","year":"2024","_id":"63346","user_id":"7888","department":[{"_id":"156"}],"type":"journal_article","status":"public","date_updated":"2025-12-22T10:40:28Z","author":[{"first_name":"Thomas","last_name":"Borgert","id":"83141","full_name":"Borgert, Thomas"},{"last_name":"Köhler","full_name":"Köhler, D","first_name":"D"},{"last_name":"Wiens","id":"7888","full_name":"Wiens, Eugen","first_name":"Eugen"},{"first_name":"R","full_name":"Kupfer, R","last_name":"Kupfer"},{"first_name":"J","last_name":"Troschitz","full_name":"Troschitz, J"},{"first_name":"Werner","id":"233","full_name":"Homberg, Werner","last_name":"Homberg"},{"first_name":"M","last_name":"Gude","full_name":"Gude, M"}],"volume":238,"doi":"10.1177/14644207241232233","publication_status":"published","publication_identifier":{"issn":["1464-4207","2041-3076"]},"citation":{"ama":"Borgert T, Köhler D, Wiens E, et al. In-situ computed tomography analysis of the failure mechanisms of thermomechanically manufactured joints with auxiliary joining element. <i>Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications</i>. 2024;238(12):2299-2306. doi:<a href=\"https://doi.org/10.1177/14644207241232233\">10.1177/14644207241232233</a>","ieee":"T. Borgert <i>et al.</i>, “In-situ computed tomography analysis of the failure mechanisms of thermomechanically manufactured joints with auxiliary joining element,” <i>Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications</i>, vol. 238, no. 12, pp. 2299–2306, 2024, doi: <a href=\"https://doi.org/10.1177/14644207241232233\">10.1177/14644207241232233</a>.","chicago":"Borgert, Thomas, D Köhler, Eugen Wiens, R Kupfer, J Troschitz, Werner Homberg, and M Gude. “In-Situ Computed Tomography Analysis of the Failure Mechanisms of Thermomechanically Manufactured Joints with Auxiliary Joining Element.” <i>Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications</i> 238, no. 12 (2024): 2299–2306. <a href=\"https://doi.org/10.1177/14644207241232233\">https://doi.org/10.1177/14644207241232233</a>.","mla":"Borgert, Thomas, et al. “In-Situ Computed Tomography Analysis of the Failure Mechanisms of Thermomechanically Manufactured Joints with Auxiliary Joining Element.” <i>Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications</i>, vol. 238, no. 12, SAGE Publications, 2024, pp. 2299–306, doi:<a href=\"https://doi.org/10.1177/14644207241232233\">10.1177/14644207241232233</a>.","short":"T. Borgert, D. Köhler, E. Wiens, R. Kupfer, J. Troschitz, W. Homberg, M. Gude, Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 238 (2024) 2299–2306.","bibtex":"@article{Borgert_Köhler_Wiens_Kupfer_Troschitz_Homberg_Gude_2024, title={In-situ computed tomography analysis of the failure mechanisms of thermomechanically manufactured joints with auxiliary joining element}, volume={238}, DOI={<a href=\"https://doi.org/10.1177/14644207241232233\">10.1177/14644207241232233</a>}, number={12}, journal={Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications}, publisher={SAGE Publications}, author={Borgert, Thomas and Köhler, D and Wiens, Eugen and Kupfer, R and Troschitz, J and Homberg, Werner and Gude, M}, year={2024}, pages={2299–2306} }","apa":"Borgert, T., Köhler, D., Wiens, E., Kupfer, R., Troschitz, J., Homberg, W., &#38; Gude, M. (2024). In-situ computed tomography analysis of the failure mechanisms of thermomechanically manufactured joints with auxiliary joining element. <i>Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications</i>, <i>238</i>(12), 2299–2306. <a href=\"https://doi.org/10.1177/14644207241232233\">https://doi.org/10.1177/14644207241232233</a>"},"page":"2299-2306","intvolume":"       238"},{"ddc":["620"],"language":[{"iso":"ger"}],"publication":"Fortschritte der Akustik - DAGA 2024","abstract":[{"text":"Piezoelektrische Keramiken finden sowohl in Sensoren als auch in Aktoren Anwendung. Bei Hochleistungs-Ultraschallanwendungen sind diese Komponenten erheblichen elektrischen und mechanischen Belastungen ausgesetzt, was zum Auftreten nichtlinearer Effekte führt. Um das nichtlineare Materialverhalten piezoelektrischer Keramiken zu charakterisieren, kann eine statische mechanische Last aufgebracht werden, die den mechanischen Arbeitspunkt verschiebt. Durch Variation dieser statischen mechanischen Belastung kann das lineare Verhalten in jedem Betriebspunkt charakterisiert werden, woraufhin die nichtlinearen Eigenschaften des Materials angenähert werden können. Allerdings ist die Sicherstellung einer homogenen mechanischen Last anspruchsvoll. Alternativ kann eine hydrostatische Belastung realisiert werden, indem die Probe in einen Behälter gegeben wird, der mit unter Druck stehendem Fluid gefüllt ist. Dadurch wird eine gleichmäßige Lastverteilung über die Oberfläche der Probe erreicht.\r\n\r\nIn diesem Beitrag wird ein Versuchsaufbau zur Durchführung elektrischer Impedanzmessungen an piezoelektrischen Keramiken in einem Druckbehälter vorgestellt. Die Probe wird im Inneren des Druckbehälters elektrisch kontaktiert. Unter Verwendung von unter Druck stehendem Argon wird auf diese Weise die Messung der elektrischen Impedanz unter hydrostatischer Last von bis zu 200 bar ermöglicht. Anschließend wird ein inverses Verfahren angewendet, um die Materialparameter in Abhängigkeit von der aufgebrachten Last zu ermitteln.","lang":"ger"}],"file":[{"relation":"main_file","content_type":"application/pdf","file_id":"53826","file_name":"daga2024friesen.pdf","access_level":"open_access","file_size":453108,"creator":"ofriesen","date_created":"2024-05-02T13:38:37Z","date_updated":"2024-05-02T14:07:24Z"}],"date_created":"2024-05-02T13:25:29Z","title":"Untersuchung piezoelektrischer Materialeigenschaften unter hydrostatischer Last","year":"2024","_id":"53822","project":[{"name":"FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)","_id":"245"}],"user_id":"11829","file_date_updated":"2024-05-02T14:07:24Z","type":"conference","status":"public","oa":"1","date_updated":"2026-01-05T07:56:21Z","author":[{"last_name":"Friesen","id":"44026","full_name":"Friesen, Olga","first_name":"Olga"},{"first_name":"Muhammad Ahsan","last_name":"Pasha","full_name":"Pasha, Muhammad Ahsan"},{"full_name":"Schwengelbeck, Max","last_name":"Schwengelbeck","first_name":"Max"},{"full_name":"Claes, Leander","id":"11829","orcid":"0000-0002-4393-268X","last_name":"Claes","first_name":"Leander"},{"first_name":"Elmar","last_name":"Baumhögger","full_name":"Baumhögger, Elmar","id":"15164"},{"first_name":"Bernd","last_name":"Henning","full_name":"Henning, Bernd","id":"213"}],"conference":{"end_date":"2024-03-21","location":"Hannover","name":"DAGA 2024 - 50. JAHRESTAGUNG FÜR AKUSTIK","start_date":"2024-03-18"},"has_accepted_license":"1","publication_status":"published","page":"1117–1120","citation":{"ama":"Friesen O, Pasha MA, Schwengelbeck M, Claes L, Baumhögger E, Henning B. Untersuchung piezoelektrischer Materialeigenschaften unter hydrostatischer Last. In: <i>Fortschritte der Akustik - DAGA 2024</i>. ; 2024:1117–1120.","chicago":"Friesen, Olga, Muhammad Ahsan Pasha, Max Schwengelbeck, Leander Claes, Elmar Baumhögger, and Bernd Henning. “Untersuchung piezoelektrischer Materialeigenschaften unter hydrostatischer Last.” In <i>Fortschritte der Akustik - DAGA 2024</i>, 1117–1120, 2024.","ieee":"O. Friesen, M. A. Pasha, M. Schwengelbeck, L. Claes, E. Baumhögger, and B. Henning, “Untersuchung piezoelektrischer Materialeigenschaften unter hydrostatischer Last,” in <i>Fortschritte der Akustik - DAGA 2024</i>, Hannover, 2024, pp. 1117–1120.","short":"O. Friesen, M.A. Pasha, M. Schwengelbeck, L. Claes, E. Baumhögger, B. Henning, in: Fortschritte der Akustik - DAGA 2024, 2024, pp. 1117–1120.","bibtex":"@inproceedings{Friesen_Pasha_Schwengelbeck_Claes_Baumhögger_Henning_2024, title={Untersuchung piezoelektrischer Materialeigenschaften unter hydrostatischer Last}, booktitle={Fortschritte der Akustik - DAGA 2024}, author={Friesen, Olga and Pasha, Muhammad Ahsan and Schwengelbeck, Max and Claes, Leander and Baumhögger, Elmar and Henning, Bernd}, year={2024}, pages={1117–1120} }","mla":"Friesen, Olga, et al. “Untersuchung piezoelektrischer Materialeigenschaften unter hydrostatischer Last.” <i>Fortschritte der Akustik - DAGA 2024</i>, 2024, pp. 1117–1120.","apa":"Friesen, O., Pasha, M. A., Schwengelbeck, M., Claes, L., Baumhögger, E., &#38; Henning, B. (2024). Untersuchung piezoelektrischer Materialeigenschaften unter hydrostatischer Last. <i>Fortschritte der Akustik - DAGA 2024</i>, 1117–1120."}},{"_id":"53824","project":[{"name":"ChaMP: Ein modellbasiertes Messverfahren zur Charakterisierung der frequenzabhängigen Materialeigenschaften von Piezokeramiken unter Verwendung eines einzelnen Probekörperindividuums","_id":"90"},{"name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"},{"name":"FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)","_id":"245"}],"department":[{"_id":"49"}],"user_id":"11829","ddc":["620"],"language":[{"iso":"ger"}],"file_date_updated":"2024-05-02T14:06:28Z","publication":"Fortschritte der Akustik - DAGA 2024","type":"conference","editor":[{"last_name":"Gesellschaft für Akustik e.V.","full_name":"Gesellschaft für Akustik e.V., Deutsche ","first_name":"Deutsche "}],"status":"public","file":[{"file_size":365911,"access_level":"open_access","file_name":"daga2024koch.pdf","file_id":"53825","date_updated":"2024-05-02T14:06:28Z","creator":"leanderc","date_created":"2024-05-02T13:36:51Z","relation":"main_file","content_type":"application/pdf"}],"oa":"1","date_updated":"2026-01-05T07:56:42Z","author":[{"first_name":"Kevin","full_name":"Koch, Kevin","last_name":"Koch"},{"id":"11829","full_name":"Claes, Leander","last_name":"Claes","orcid":"0000-0002-4393-268X","first_name":"Leander"},{"full_name":"Jurgelucks, Benjamin","last_name":"Jurgelucks","first_name":"Benjamin"},{"first_name":"Lars","last_name":"Meihost","id":"24769","full_name":"Meihost, Lars"},{"last_name":"Henning","full_name":"Henning, Bernd","id":"213","first_name":"Bernd"}],"date_created":"2024-05-02T13:34:01Z","title":"Inverses Verfahren zur Identifikation piezoelektrischer Materialparameter unterstützt durch neuronale Netze","conference":{"start_date":"2024-03-18","end_date":"2024-03-21"},"has_accepted_license":"1","year":"2024","page":"1113–1116","citation":{"ama":"Koch K, Claes L, Jurgelucks B, Meihost L, Henning B. Inverses Verfahren zur Identifikation piezoelektrischer Materialparameter unterstützt durch neuronale Netze. In: Gesellschaft für Akustik e.V. D, ed. <i>Fortschritte der Akustik - DAGA 2024</i>. ; 2024:1113–1116.","ieee":"K. Koch, L. Claes, B. Jurgelucks, L. Meihost, and B. Henning, “Inverses Verfahren zur Identifikation piezoelektrischer Materialparameter unterstützt durch neuronale Netze,” in <i>Fortschritte der Akustik - DAGA 2024</i>, 2024, pp. 1113–1116.","chicago":"Koch, Kevin, Leander Claes, Benjamin Jurgelucks, Lars Meihost, and Bernd Henning. “Inverses Verfahren zur Identifikation piezoelektrischer Materialparameter unterstützt durch neuronale Netze.” In <i>Fortschritte der Akustik - DAGA 2024</i>, edited by Deutsche  Gesellschaft für Akustik e.V., 1113–1116, 2024.","apa":"Koch, K., Claes, L., Jurgelucks, B., Meihost, L., &#38; Henning, B. (2024). Inverses Verfahren zur Identifikation piezoelektrischer Materialparameter unterstützt durch neuronale Netze. In D. Gesellschaft für Akustik e.V. (Ed.), <i>Fortschritte der Akustik - DAGA 2024</i> (pp. 1113–1116).","bibtex":"@inproceedings{Koch_Claes_Jurgelucks_Meihost_Henning_2024, title={Inverses Verfahren zur Identifikation piezoelektrischer Materialparameter unterstützt durch neuronale Netze}, booktitle={Fortschritte der Akustik - DAGA 2024}, author={Koch, Kevin and Claes, Leander and Jurgelucks, Benjamin and Meihost, Lars and Henning, Bernd}, editor={Gesellschaft für Akustik e.V., Deutsche }, year={2024}, pages={1113–1116} }","short":"K. Koch, L. Claes, B. Jurgelucks, L. Meihost, B. Henning, in: D. Gesellschaft für Akustik e.V. (Ed.), Fortschritte der Akustik - DAGA 2024, 2024, pp. 1113–1116.","mla":"Koch, Kevin, et al. “Inverses Verfahren zur Identifikation piezoelektrischer Materialparameter unterstützt durch neuronale Netze.” <i>Fortschritte der Akustik - DAGA 2024</i>, edited by Deutsche  Gesellschaft für Akustik e.V., 2024, pp. 1113–1116."}},{"status":"public","type":"conference","publication":"2023 International Congress on Ultrasonics, Beijing, China","language":[{"iso":"eng"}],"project":[{"_id":"245","name":"FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)"}],"_id":"56834","user_id":"11829","department":[{"_id":"49"}],"year":"2024","citation":{"chicago":"Friesen, Olga, Leander Claes, Claus Scheidemann, Nadine Feldmann, Tobias Hemsel, and Bernd Henning. “Estimation of Temperature-Dependent Piezoelectric Material Parameters Using Ring-Shaped Specimens.” In <i>2023 International Congress on Ultrasonics, Beijing, China</i>, 2822:012125. IOP Publishing, 2024. <a href=\"https://doi.org/10.1088/1742-6596/2822/1/012125\">https://doi.org/10.1088/1742-6596/2822/1/012125</a>.","ieee":"O. Friesen, L. Claes, C. Scheidemann, N. Feldmann, T. Hemsel, and B. Henning, “Estimation of temperature-dependent piezoelectric material parameters using ring-shaped specimens,” in <i>2023 International Congress on Ultrasonics, Beijing, China</i>, 2024, vol. 2822, p. 012125, doi: <a href=\"https://doi.org/10.1088/1742-6596/2822/1/012125\">10.1088/1742-6596/2822/1/012125</a>.","ama":"Friesen O, Claes L, Scheidemann C, Feldmann N, Hemsel T, Henning B. Estimation of temperature-dependent piezoelectric material parameters using ring-shaped specimens. In: <i>2023 International Congress on Ultrasonics, Beijing, China</i>. Vol 2822. IOP Publishing; 2024:012125. doi:<a href=\"https://doi.org/10.1088/1742-6596/2822/1/012125\">10.1088/1742-6596/2822/1/012125</a>","apa":"Friesen, O., Claes, L., Scheidemann, C., Feldmann, N., Hemsel, T., &#38; Henning, B. (2024). Estimation of temperature-dependent piezoelectric material parameters using ring-shaped specimens. <i>2023 International Congress on Ultrasonics, Beijing, China</i>, <i>2822</i>, 012125. <a href=\"https://doi.org/10.1088/1742-6596/2822/1/012125\">https://doi.org/10.1088/1742-6596/2822/1/012125</a>","mla":"Friesen, Olga, et al. “Estimation of Temperature-Dependent Piezoelectric Material Parameters Using Ring-Shaped Specimens.” <i>2023 International Congress on Ultrasonics, Beijing, China</i>, vol. 2822, IOP Publishing, 2024, p. 012125, doi:<a href=\"https://doi.org/10.1088/1742-6596/2822/1/012125\">10.1088/1742-6596/2822/1/012125</a>.","short":"O. Friesen, L. Claes, C. Scheidemann, N. Feldmann, T. Hemsel, B. Henning, in: 2023 International Congress on Ultrasonics, Beijing, China, IOP Publishing, 2024, p. 012125.","bibtex":"@inproceedings{Friesen_Claes_Scheidemann_Feldmann_Hemsel_Henning_2024, title={Estimation of temperature-dependent piezoelectric material parameters using ring-shaped specimens}, volume={2822}, DOI={<a href=\"https://doi.org/10.1088/1742-6596/2822/1/012125\">10.1088/1742-6596/2822/1/012125</a>}, booktitle={2023 International Congress on Ultrasonics, Beijing, China}, publisher={IOP Publishing}, author={Friesen, Olga and Claes, Leander and Scheidemann, Claus and Feldmann, Nadine and Hemsel, Tobias and Henning, Bernd}, year={2024}, pages={012125} }"},"intvolume":"      2822","page":"012125","publication_identifier":{"issn":["1742-6596"]},"title":"Estimation of temperature-dependent piezoelectric material parameters using ring-shaped specimens","main_file_link":[{"url":"https://iopscience.iop.org/article/10.1088/1742-6596/2822/1/012125","open_access":"1"}],"doi":"10.1088/1742-6596/2822/1/012125","publisher":"IOP Publishing","oa":"1","date_updated":"2026-01-05T07:58:55Z","date_created":"2024-10-31T07:59:01Z","author":[{"id":"44026","full_name":"Friesen, Olga","last_name":"Friesen","first_name":"Olga"},{"first_name":"Leander","last_name":"Claes","orcid":"0000-0002-4393-268X","id":"11829","full_name":"Claes, Leander"},{"last_name":"Scheidemann","id":"38259","full_name":"Scheidemann, Claus","first_name":"Claus"},{"last_name":"Feldmann","id":"23082","full_name":"Feldmann, Nadine","first_name":"Nadine"},{"first_name":"Tobias","last_name":"Hemsel","id":"210","full_name":"Hemsel, Tobias"},{"first_name":"Bernd","id":"213","full_name":"Henning, Bernd","last_name":"Henning"}],"volume":2822},{"title":"Randomised material parameter impedance dataset of piezoelectric rings","doi":"10.5281/zenodo.13143680","date_updated":"2026-01-05T07:57:46Z","publisher":"Zenodo","author":[{"first_name":"Kevin","full_name":"Koch, Kevin","last_name":"Koch"},{"first_name":"Olga","last_name":"Friesen","id":"44026","full_name":"Friesen, Olga"},{"full_name":"Claes, Leander","id":"11829","last_name":"Claes","orcid":"0000-0002-4393-268X","first_name":"Leander"}],"date_created":"2024-07-31T14:10:12Z","year":"2024","citation":{"chicago":"Koch, Kevin, Olga Friesen, and Leander Claes. <i>Randomised Material Parameter Impedance Dataset of Piezoelectric Rings</i>. Zenodo, 2024. <a href=\"https://doi.org/10.5281/zenodo.13143680\">https://doi.org/10.5281/zenodo.13143680</a>.","ieee":"K. Koch, O. Friesen, and L. Claes, <i>Randomised material parameter impedance dataset of piezoelectric rings</i>. Zenodo, 2024.","ama":"Koch K, Friesen O, Claes L. <i>Randomised Material Parameter Impedance Dataset of Piezoelectric Rings</i>. Zenodo; 2024. doi:<a href=\"https://doi.org/10.5281/zenodo.13143680\">10.5281/zenodo.13143680</a>","apa":"Koch, K., Friesen, O., &#38; Claes, L. (2024). <i>Randomised material parameter impedance dataset of piezoelectric rings</i>. Zenodo. <a href=\"https://doi.org/10.5281/zenodo.13143680\">https://doi.org/10.5281/zenodo.13143680</a>","bibtex":"@book{Koch_Friesen_Claes_2024, title={Randomised material parameter impedance dataset of piezoelectric rings}, DOI={<a href=\"https://doi.org/10.5281/zenodo.13143680\">10.5281/zenodo.13143680</a>}, publisher={Zenodo}, author={Koch, Kevin and Friesen, Olga and Claes, Leander}, year={2024} }","short":"K. Koch, O. Friesen, L. Claes, Randomised Material Parameter Impedance Dataset of Piezoelectric Rings, Zenodo, 2024.","mla":"Koch, Kevin, et al. <i>Randomised Material Parameter Impedance Dataset of Piezoelectric Rings</i>. Zenodo, 2024, doi:<a href=\"https://doi.org/10.5281/zenodo.13143680\">10.5281/zenodo.13143680</a>."},"_id":"55470","project":[{"name":"ChaMP: Ein modellbasiertes Messverfahren zur Charakterisierung der frequenzabhängigen Materialeigenschaften von Piezokeramiken unter Verwendung eines einzelnen Probekörperindividuums","_id":"90"},{"_id":"52","name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing"},{"name":"FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)","_id":"245"}],"department":[{"_id":"49"}],"user_id":"11829","status":"public","type":"research_data"},{"_id":"53662","project":[{"name":"ChaMP: Ein modellbasiertes Messverfahren zur Charakterisierung der frequenzabhängigen Materialeigenschaften von Piezokeramiken unter Verwendung eines einzelnen Probekörperindividuums","_id":"90"},{"_id":"52","name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing"},{"name":"FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)","_id":"245"}],"department":[{"_id":"49"}],"user_id":"11829","status":"public","type":"research_data","title":"Randomised material parameter piezoelectric impedance dataset with structured electrodes","doi":"10.5281/ZENODO.11064206","publisher":"zenodo","date_updated":"2026-01-05T07:56:58Z","date_created":"2024-04-25T13:54:49Z","author":[{"last_name":"Koch","full_name":"Koch, Kevin","first_name":"Kevin"},{"first_name":"Leander","id":"11829","full_name":"Claes, Leander","last_name":"Claes","orcid":"0000-0002-4393-268X"}],"year":"2024","citation":{"ieee":"K. Koch and L. Claes, <i>Randomised material parameter piezoelectric impedance dataset with structured electrodes</i>. zenodo, 2024.","chicago":"Koch, Kevin, and Leander Claes. <i>Randomised Material Parameter Piezoelectric Impedance Dataset with Structured Electrodes</i>. zenodo, 2024. <a href=\"https://doi.org/10.5281/ZENODO.11064206\">https://doi.org/10.5281/ZENODO.11064206</a>.","ama":"Koch K, Claes L. <i>Randomised Material Parameter Piezoelectric Impedance Dataset with Structured Electrodes</i>. zenodo; 2024. doi:<a href=\"https://doi.org/10.5281/ZENODO.11064206\">10.5281/ZENODO.11064206</a>","mla":"Koch, Kevin, and Leander Claes. <i>Randomised Material Parameter Piezoelectric Impedance Dataset with Structured Electrodes</i>. zenodo, 2024, doi:<a href=\"https://doi.org/10.5281/ZENODO.11064206\">10.5281/ZENODO.11064206</a>.","short":"K. Koch, L. Claes, Randomised Material Parameter Piezoelectric Impedance Dataset with Structured Electrodes, zenodo, 2024.","bibtex":"@book{Koch_Claes_2024, title={Randomised material parameter piezoelectric impedance dataset with structured electrodes}, DOI={<a href=\"https://doi.org/10.5281/ZENODO.11064206\">10.5281/ZENODO.11064206</a>}, publisher={zenodo}, author={Koch, Kevin and Claes, Leander}, year={2024} }","apa":"Koch, K., &#38; Claes, L. (2024). <i>Randomised material parameter piezoelectric impedance dataset with structured electrodes</i>. zenodo. <a href=\"https://doi.org/10.5281/ZENODO.11064206\">https://doi.org/10.5281/ZENODO.11064206</a>"}},{"status":"public","type":"misc","language":[{"iso":"eng"}],"project":[{"_id":"52","name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing"},{"_id":"245","name":"FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)"}],"_id":"55416","user_id":"11829","department":[{"_id":"49"}],"year":"2024","place":"International Workshop on Piezoelectric Materials and Applications (IWPMA)","citation":{"short":"L. Claes, K. Koch, O. Friesen, L. Meihost, Machine Learning in Inverse Measurement Problems: An Application to Piezoelectric Material Characterisation, International Workshop on Piezoelectric Materials and Applications (IWPMA), 2024.","mla":"Claes, Leander, et al. <i>Machine Learning in Inverse Measurement Problems: An Application to Piezoelectric Material Characterisation</i>. 2024.","bibtex":"@book{Claes_Koch_Friesen_Meihost_2024, place={International Workshop on Piezoelectric Materials and Applications (IWPMA)}, title={Machine learning in inverse measurement problems: An application to piezoelectric material characterisation}, author={Claes, Leander and Koch, Kevin and Friesen, Olga and Meihost, Lars}, year={2024} }","apa":"Claes, L., Koch, K., Friesen, O., &#38; Meihost, L. (2024). <i>Machine learning in inverse measurement problems: An application to piezoelectric material characterisation</i>.","ama":"Claes L, Koch K, Friesen O, Meihost L. <i>Machine Learning in Inverse Measurement Problems: An Application to Piezoelectric Material Characterisation</i>.; 2024.","chicago":"Claes, Leander, Kevin Koch, Olga Friesen, and Lars Meihost. <i>Machine Learning in Inverse Measurement Problems: An Application to Piezoelectric Material Characterisation</i>. International Workshop on Piezoelectric Materials and Applications (IWPMA), 2024.","ieee":"L. Claes, K. Koch, O. Friesen, and L. Meihost, <i>Machine learning in inverse measurement problems: An application to piezoelectric material characterisation</i>. International Workshop on Piezoelectric Materials and Applications (IWPMA), 2024."},"title":"Machine learning in inverse measurement problems: An application to piezoelectric material characterisation","date_updated":"2026-01-05T07:57:27Z","author":[{"first_name":"Leander","full_name":"Claes, Leander","id":"11829","last_name":"Claes","orcid":"0000-0002-4393-268X"},{"last_name":"Koch","full_name":"Koch, Kevin","first_name":"Kevin"},{"full_name":"Friesen, Olga","id":"44026","last_name":"Friesen","first_name":"Olga"},{"first_name":"Lars","last_name":"Meihost","id":"24769","full_name":"Meihost, Lars"}],"date_created":"2024-07-29T12:34:21Z"},{"year":"2024","citation":{"apa":"Friesen, O., Claes, L., Feldmann, N., &#38; Henning, B. (2024). Estimation of piezoelectric material parameters of ring-shaped specimens. <i>Tm - Technisches Messen</i>. <a href=\"https://doi.org/10.1515/teme-2024-0107\">https://doi.org/10.1515/teme-2024-0107</a>","short":"O. Friesen, L. Claes, N. Feldmann, B. Henning, Tm - Technisches Messen (2024).","mla":"Friesen, Olga, et al. “Estimation of Piezoelectric Material Parameters of Ring-Shaped Specimens.” <i>Tm - Technisches Messen</i>, De Gruyter, 2024, doi:<a href=\"https://doi.org/10.1515/teme-2024-0107\">https://doi.org/10.1515/teme-2024-0107</a>.","bibtex":"@article{Friesen_Claes_Feldmann_Henning_2024, title={Estimation of piezoelectric material parameters of ring-shaped specimens}, DOI={<a href=\"https://doi.org/10.1515/teme-2024-0107\">https://doi.org/10.1515/teme-2024-0107</a>}, journal={tm - Technisches Messen}, publisher={De Gruyter}, author={Friesen, Olga and Claes, Leander and Feldmann, Nadine and Henning, Bernd}, year={2024} }","chicago":"Friesen, Olga, Leander Claes, Nadine Feldmann, and Bernd Henning. “Estimation of Piezoelectric Material Parameters of Ring-Shaped Specimens.” <i>Tm - Technisches Messen</i>, 2024. <a href=\"https://doi.org/10.1515/teme-2024-0107\">https://doi.org/10.1515/teme-2024-0107</a>.","ieee":"O. Friesen, L. Claes, N. Feldmann, and B. Henning, “Estimation of piezoelectric material parameters of ring-shaped specimens,” <i>tm - Technisches Messen</i>, 2024, doi: <a href=\"https://doi.org/10.1515/teme-2024-0107\">https://doi.org/10.1515/teme-2024-0107</a>.","ama":"Friesen O, Claes L, Feldmann N, Henning B. Estimation of piezoelectric material parameters of ring-shaped specimens. <i>tm - Technisches Messen</i>. Published online 2024. doi:<a href=\"https://doi.org/10.1515/teme-2024-0107\">https://doi.org/10.1515/teme-2024-0107</a>"},"publication_identifier":{"issn":["2196-7113"]},"publication_status":"published","title":"Estimation of piezoelectric material parameters of ring-shaped specimens","doi":"https://doi.org/10.1515/teme-2024-0107","date_updated":"2026-01-05T07:59:24Z","publisher":"De Gruyter","author":[{"first_name":"Olga","full_name":"Friesen, Olga","id":"44026","last_name":"Friesen"},{"full_name":"Claes, Leander","id":"11829","orcid":"0000-0002-4393-268X","last_name":"Claes","first_name":"Leander"},{"full_name":"Feldmann, Nadine","id":"23082","last_name":"Feldmann","first_name":"Nadine"},{"last_name":"Henning","id":"213","full_name":"Henning, Bernd","first_name":"Bernd"}],"date_created":"2024-10-29T09:07:00Z","abstract":[{"lang":"eng","text":"The estimation of accurate piezoelectric material parameters is a fundamental prerequisite for simulation-driven design of piezoelectric actuators and sensors. Previous studies show that a full set of material parameters can be determined in an inverse procedure using a single disc-shaped specimen with an electrode structured for increased sensitivity with respect to all material parameters. However, in the case of high-power actuator applications, ring-shaped piezoelectric components are often employed, necessitating an adaptation of the previously developed method. The alteration in geometry introduces some advantages. Accordingly, there is no longer any requirement to modify the electrode structure in order to enhance sensitivity. The method to estimate the material parameters presented here consists of a total of three stages. An initial, approximate estimation of the material parameters is determined using analytical approximations for the resonance frequencies from the IEEE standard. These values are optimised in an inverse procedure that employs analytic expressions for the electrical impedance of piezoelectric rings as the forward model. Further refinement is achieved by using Finite Element (FE) simulations as the forward model again in an inverse procedure. The method is applied to electrical impedance measurement data, yielding material parameters for hard piezoelectric rings. The result shows a good agreement between the simulation and measurement results, indicating realistic material parameter values."}],"status":"public","publication":"tm - Technisches Messen","type":"journal_article","language":[{"iso":"eng"}],"_id":"56777","project":[{"_id":"245","name":"FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)"}],"department":[{"_id":"49"}],"user_id":"11829"},{"article_type":"original","alternative_title":["Neural networks for initial value estimation in the identification of piezoelectric material parameters"],"language":[{"iso":"eng"}],"project":[{"_id":"90","name":"ChaMP: Ein modellbasiertes Messverfahren zur Charakterisierung der frequenzabhängigen Materialeigenschaften von Piezokeramiken unter Verwendung eines einzelnen Probekörperindividuums"},{"_id":"52","name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing"},{"name":"FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)","_id":"245"}],"_id":"54314","user_id":"11829","department":[{"_id":"49"}],"status":"public","type":"journal_article","publication":"tm - Technisches Messen","title":"Neuronale Netze zur Startwertschätzung bei der Identifikation piezoelektrischer Materialparameter","main_file_link":[{"url":"https://www.degruyter.com/document/doi/10.1515/teme-2024-0099/html"}],"doi":"10.1515/teme-2024-0099","date_updated":"2026-01-05T07:59:09Z","publisher":"Walter de Gruyter GmbH","date_created":"2024-05-17T08:26:55Z","author":[{"first_name":"Kevin","last_name":"Koch","full_name":"Koch, Kevin"},{"first_name":"Leander","full_name":"Claes, Leander","id":"11829","last_name":"Claes","orcid":"0000-0002-4393-268X"},{"first_name":"Benjamin","last_name":"Jurgelucks","full_name":"Jurgelucks, Benjamin"},{"id":"24769","full_name":"Meihost, Lars","last_name":"Meihost","first_name":"Lars"}],"year":"2024","citation":{"chicago":"Koch, Kevin, Leander Claes, Benjamin Jurgelucks, and Lars Meihost. “Neuronale Netze Zur Startwertschätzung Bei Der Identifikation Piezoelektrischer Materialparameter.” <i>Tm - Technisches Messen</i>, 2024. <a href=\"https://doi.org/10.1515/teme-2024-0099\">https://doi.org/10.1515/teme-2024-0099</a>.","ieee":"K. Koch, L. Claes, B. Jurgelucks, and L. Meihost, “Neuronale Netze zur Startwertschätzung bei der Identifikation piezoelektrischer Materialparameter,” <i>tm - Technisches Messen</i>, 2024, doi: <a href=\"https://doi.org/10.1515/teme-2024-0099\">10.1515/teme-2024-0099</a>.","ama":"Koch K, Claes L, Jurgelucks B, Meihost L. Neuronale Netze zur Startwertschätzung bei der Identifikation piezoelektrischer Materialparameter. <i>tm - Technisches Messen</i>. Published online 2024. doi:<a href=\"https://doi.org/10.1515/teme-2024-0099\">10.1515/teme-2024-0099</a>","apa":"Koch, K., Claes, L., Jurgelucks, B., &#38; Meihost, L. (2024). Neuronale Netze zur Startwertschätzung bei der Identifikation piezoelektrischer Materialparameter. <i>Tm - Technisches Messen</i>. <a href=\"https://doi.org/10.1515/teme-2024-0099\">https://doi.org/10.1515/teme-2024-0099</a>","bibtex":"@article{Koch_Claes_Jurgelucks_Meihost_2024, title={Neuronale Netze zur Startwertschätzung bei der Identifikation piezoelektrischer Materialparameter}, DOI={<a href=\"https://doi.org/10.1515/teme-2024-0099\">10.1515/teme-2024-0099</a>}, journal={tm - Technisches Messen}, publisher={Walter de Gruyter GmbH}, author={Koch, Kevin and Claes, Leander and Jurgelucks, Benjamin and Meihost, Lars}, year={2024} }","short":"K. Koch, L. Claes, B. Jurgelucks, L. Meihost, Tm - Technisches Messen (2024).","mla":"Koch, Kevin, et al. “Neuronale Netze Zur Startwertschätzung Bei Der Identifikation Piezoelektrischer Materialparameter.” <i>Tm - Technisches Messen</i>, Walter de Gruyter GmbH, 2024, doi:<a href=\"https://doi.org/10.1515/teme-2024-0099\">10.1515/teme-2024-0099</a>."},"quality_controlled":"1"},{"language":[{"iso":"eng"}],"article_number":"113600","user_id":"11829","department":[{"_id":"90"}],"project":[{"name":"FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)","_id":"245"}],"_id":"57820","status":"public","type":"journal_article","publication":"Nonlinear Analysis","doi":"10.1016/j.na.2024.113600","title":"L∞ blow-up in the Jordan-Moore-Gibson-Thompson equation","author":[{"first_name":"Vanja","last_name":"Nikolić","full_name":"Nikolić, Vanja"},{"last_name":"Winkler","id":"31496","full_name":"Winkler, Michael","first_name":"Michael"}],"date_created":"2024-12-18T07:13:19Z","volume":247,"publisher":"Elsevier BV","date_updated":"2026-01-05T08:02:36Z","citation":{"ama":"Nikolić V, Winkler M. L∞ blow-up in the Jordan-Moore-Gibson-Thompson equation. <i>Nonlinear Analysis</i>. 2024;247. doi:<a href=\"https://doi.org/10.1016/j.na.2024.113600\">10.1016/j.na.2024.113600</a>","chicago":"Nikolić, Vanja, and Michael Winkler. “L∞ Blow-up in the Jordan-Moore-Gibson-Thompson Equation.” <i>Nonlinear Analysis</i> 247 (2024). <a href=\"https://doi.org/10.1016/j.na.2024.113600\">https://doi.org/10.1016/j.na.2024.113600</a>.","ieee":"V. Nikolić and M. Winkler, “L∞ blow-up in the Jordan-Moore-Gibson-Thompson equation,” <i>Nonlinear Analysis</i>, vol. 247, Art. no. 113600, 2024, doi: <a href=\"https://doi.org/10.1016/j.na.2024.113600\">10.1016/j.na.2024.113600</a>.","apa":"Nikolić, V., &#38; Winkler, M. (2024). L∞ blow-up in the Jordan-Moore-Gibson-Thompson equation. <i>Nonlinear Analysis</i>, <i>247</i>, Article 113600. <a href=\"https://doi.org/10.1016/j.na.2024.113600\">https://doi.org/10.1016/j.na.2024.113600</a>","mla":"Nikolić, Vanja, and Michael Winkler. “L∞ Blow-up in the Jordan-Moore-Gibson-Thompson Equation.” <i>Nonlinear Analysis</i>, vol. 247, 113600, Elsevier BV, 2024, doi:<a href=\"https://doi.org/10.1016/j.na.2024.113600\">10.1016/j.na.2024.113600</a>.","bibtex":"@article{Nikolić_Winkler_2024, title={L∞ blow-up in the Jordan-Moore-Gibson-Thompson equation}, volume={247}, DOI={<a href=\"https://doi.org/10.1016/j.na.2024.113600\">10.1016/j.na.2024.113600</a>}, number={113600}, journal={Nonlinear Analysis}, publisher={Elsevier BV}, author={Nikolić, Vanja and Winkler, Michael}, year={2024} }","short":"V. Nikolić, M. Winkler, Nonlinear Analysis 247 (2024)."},"intvolume":"       247","year":"2024","publication_status":"published","publication_identifier":{"issn":["0362-546X"]}}]
