[{"_id":"53319","user_id":"31496","keyword":["General Mathematics"],"language":[{"iso":"eng"}],"publication":"International Mathematics Research Notices","type":"journal_article","abstract":[{"text":"<jats:title>Abstract</jats:title>\r\n               <jats:p>The Neumann problem for (0.1)$$ \\begin{align}&amp; V_t = \\Delta V-aV+f(x,t) \\end{align}$$is considered in bounded domains $\\Omega \\subset {\\mathbb {R}}^n$ with smooth boundary, where $n\\ge 1$ and $a\\in {\\mathbb {R}}$. By means of a variational approach, a statement on boundedness of the quantities $$ \\begin{eqnarray*} \\sup_{t\\in (0,T)} \\int_\\Omega \\big|\\nabla V(\\cdot,t)\\big|^p L^{\\frac{n+p}{n+2}} \\Big( \\big|\\nabla V(\\cdot,t)\\big| \\Big) \\end{eqnarray*}$$in dependence on the expressions (0.2)$$ \\begin{align}&amp; \\sup_{t\\in (0,T-\\tau)} \\int_t^{t+\\tau} \\int_\\Omega |f|^{\\frac{(n+2)p}{n+p}} L\\big( |f|\\big) \\end{align}$$is derived for $p\\ge 2$, $\\tau&amp;gt;0$, and $T\\ge 2\\tau $, provided that $L\\in C^0([0,\\infty ))$ is positive, strictly increasing, unbounded, and slowly growing in the sense that $\\limsup _{s\\to \\infty } \\frac {L(s^{\\lambda _0})}{L(s)} &amp;lt;\\infty $ for some $\\lambda _0&amp;gt;1$. In the particular case when $p=n\\ge 2$, an additional condition on growth of $L$, particularly satisfied by $L(\\xi ):=\\ln ^\\alpha (\\xi +b)$ whenever $b&amp;gt;0$ and $\\alpha&amp;gt;\\frac {(n+2)(n-1)}{2n}$, is identified as sufficient to ensure that as a consequence of the above, bounds for theintegrals in (0.2) even imply estimates for the spatio-temporal modulus of continuity of solutions to (0.1). A subsequent application to the Keller–Segel system $$ \\begin{eqnarray*} \\left\\{ \\begin{array}{l} u_t = \\nabla \\cdot \\big( D(v)\\nabla u\\big) - \\nabla \\cdot \\big( uS(v)\\nabla v\\big) + ru - \\mu u^2, \\\\[1mm] v_t = \\Delta v-v+u, \\end{array} \\right. \\end{eqnarray*}$$shows that when $n=2$, $r\\in {\\mathbb {R}}$, $0&amp;lt;D\\in C^2([0,\\infty ))$, and $S\\in C^2([0,\\infty )) \\cap W^{1,\\infty }((0,\\infty ))$ and thus especially in the presence of arbitrarily strong diffusion degeneracies implied by rapid decay of $D$, any choice of $\\mu&amp;gt;0$ excludes blowup in the sense that for all suitably regular nonnegative initial data, an associated initial-boundary value problem admits a global bounded classical solution.</jats:p>","lang":"eng"}],"status":"public","publisher":"Oxford University Press (OUP)","date_updated":"2024-04-07T12:36:06Z","volume":2023,"author":[{"first_name":"Michael","full_name":"Winkler, Michael","last_name":"Winkler"}],"date_created":"2024-04-07T12:33:44Z","title":"A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System","doi":"10.1093/imrn/rnac286","publication_identifier":{"issn":["1073-7928","1687-0247"]},"publication_status":"published","issue":"19","year":"2022","intvolume":"      2023","page":"16336-16393","citation":{"apa":"Winkler, M. (2022). A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System. <i>International Mathematics Research Notices</i>, <i>2023</i>(19), 16336–16393. <a href=\"https://doi.org/10.1093/imrn/rnac286\">https://doi.org/10.1093/imrn/rnac286</a>","bibtex":"@article{Winkler_2022, title={A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System}, volume={2023}, DOI={<a href=\"https://doi.org/10.1093/imrn/rnac286\">10.1093/imrn/rnac286</a>}, number={19}, journal={International Mathematics Research Notices}, publisher={Oxford University Press (OUP)}, author={Winkler, Michael}, year={2022}, pages={16336–16393} }","mla":"Winkler, Michael. “A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System.” <i>International Mathematics Research Notices</i>, vol. 2023, no. 19, Oxford University Press (OUP), 2022, pp. 16336–93, doi:<a href=\"https://doi.org/10.1093/imrn/rnac286\">10.1093/imrn/rnac286</a>.","short":"M. Winkler, International Mathematics Research Notices 2023 (2022) 16336–16393.","ama":"Winkler M. A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System. <i>International Mathematics Research Notices</i>. 2022;2023(19):16336-16393. doi:<a href=\"https://doi.org/10.1093/imrn/rnac286\">10.1093/imrn/rnac286</a>","chicago":"Winkler, Michael. “A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System.” <i>International Mathematics Research Notices</i> 2023, no. 19 (2022): 16336–93. <a href=\"https://doi.org/10.1093/imrn/rnac286\">https://doi.org/10.1093/imrn/rnac286</a>.","ieee":"M. Winkler, “A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System,” <i>International Mathematics Research Notices</i>, vol. 2023, no. 19, pp. 16336–16393, 2022, doi: <a href=\"https://doi.org/10.1093/imrn/rnac286\">10.1093/imrn/rnac286</a>."}},{"publisher":"World Scientific Pub Co Pte Ltd","date_updated":"2024-04-07T12:35:53Z","volume":25,"date_created":"2024-04-07T12:35:09Z","author":[{"first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael"}],"title":"Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems","doi":"10.1142/s0219199722500626","publication_identifier":{"issn":["0219-1997","1793-6683"]},"publication_status":"published","issue":"10","year":"2022","intvolume":"        25","citation":{"mla":"Winkler, Michael. “Arbitrarily Fast Grow-up Rates in Quasilinear Keller–Segel Systems.” <i>Communications in Contemporary Mathematics</i>, vol. 25, no. 10, World Scientific Pub Co Pte Ltd, 2022, doi:<a href=\"https://doi.org/10.1142/s0219199722500626\">10.1142/s0219199722500626</a>.","bibtex":"@article{Winkler_2022, title={Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems}, volume={25}, DOI={<a href=\"https://doi.org/10.1142/s0219199722500626\">10.1142/s0219199722500626</a>}, number={10}, journal={Communications in Contemporary Mathematics}, publisher={World Scientific Pub Co Pte Ltd}, author={Winkler, Michael}, year={2022} }","short":"M. Winkler, Communications in Contemporary Mathematics 25 (2022).","apa":"Winkler, M. (2022). Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems. <i>Communications in Contemporary Mathematics</i>, <i>25</i>(10). <a href=\"https://doi.org/10.1142/s0219199722500626\">https://doi.org/10.1142/s0219199722500626</a>","ama":"Winkler M. Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems. <i>Communications in Contemporary Mathematics</i>. 2022;25(10). doi:<a href=\"https://doi.org/10.1142/s0219199722500626\">10.1142/s0219199722500626</a>","ieee":"M. Winkler, “Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems,” <i>Communications in Contemporary Mathematics</i>, vol. 25, no. 10, 2022, doi: <a href=\"https://doi.org/10.1142/s0219199722500626\">10.1142/s0219199722500626</a>.","chicago":"Winkler, Michael. “Arbitrarily Fast Grow-up Rates in Quasilinear Keller–Segel Systems.” <i>Communications in Contemporary Mathematics</i> 25, no. 10 (2022). <a href=\"https://doi.org/10.1142/s0219199722500626\">https://doi.org/10.1142/s0219199722500626</a>."},"_id":"53321","user_id":"31496","keyword":["Applied Mathematics","General Mathematics"],"language":[{"iso":"eng"}],"publication":"Communications in Contemporary Mathematics","type":"journal_article","abstract":[{"lang":"eng","text":"<jats:p> The chemotaxis system [Formula: see text] is considered in a ball [Formula: see text], [Formula: see text], where the positive function [Formula: see text] reflects suitably weak diffusion by satisfying [Formula: see text] for some [Formula: see text]. It is shown that whenever [Formula: see text] is positive and satisfies [Formula: see text] as [Formula: see text], one can find a suitably regular nonlinearity [Formula: see text] with the property that at each sufficiently large mass level [Formula: see text] there exists a globally defined radially symmetric classical solution to a Neumann-type boundary value problem for (⋆) which satisfies [Formula: see text] </jats:p>"}],"status":"public"},{"citation":{"ama":"Winkler M. Slow Grow-up in a Quasilinear Keller–Segel System. <i>Journal of Dynamics and Differential Equations</i>. Published online 2022. doi:<a href=\"https://doi.org/10.1007/s10884-022-10167-w\">10.1007/s10884-022-10167-w</a>","chicago":"Winkler, Michael. “Slow Grow-up in a Quasilinear Keller–Segel System.” <i>Journal of Dynamics and Differential Equations</i>, 2022. <a href=\"https://doi.org/10.1007/s10884-022-10167-w\">https://doi.org/10.1007/s10884-022-10167-w</a>.","ieee":"M. Winkler, “Slow Grow-up in a Quasilinear Keller–Segel System,” <i>Journal of Dynamics and Differential Equations</i>, 2022, doi: <a href=\"https://doi.org/10.1007/s10884-022-10167-w\">10.1007/s10884-022-10167-w</a>.","apa":"Winkler, M. (2022). Slow Grow-up in a Quasilinear Keller–Segel System. <i>Journal of Dynamics and Differential Equations</i>. <a href=\"https://doi.org/10.1007/s10884-022-10167-w\">https://doi.org/10.1007/s10884-022-10167-w</a>","short":"M. Winkler, Journal of Dynamics and Differential Equations (2022).","mla":"Winkler, Michael. “Slow Grow-up in a Quasilinear Keller–Segel System.” <i>Journal of Dynamics and Differential Equations</i>, Springer Science and Business Media LLC, 2022, doi:<a href=\"https://doi.org/10.1007/s10884-022-10167-w\">10.1007/s10884-022-10167-w</a>.","bibtex":"@article{Winkler_2022, title={Slow Grow-up in a Quasilinear Keller–Segel System}, DOI={<a href=\"https://doi.org/10.1007/s10884-022-10167-w\">10.1007/s10884-022-10167-w</a>}, journal={Journal of Dynamics and Differential Equations}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2022} }"},"year":"2022","publication_identifier":{"issn":["1040-7294","1572-9222"]},"publication_status":"published","doi":"10.1007/s10884-022-10167-w","title":"Slow Grow-up in a Quasilinear Keller–Segel System","author":[{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"date_created":"2024-04-07T12:39:12Z","date_updated":"2024-04-07T12:39:17Z","publisher":"Springer Science and Business Media LLC","status":"public","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>In a ball <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\Omega =B_R(0)\\subset \\mathbb {R}^n$$</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:msub>\r\n                    <mml:mi>B</mml:mi>\r\n                    <mml:mi>R</mml:mi>\r\n                  </mml:msub>\r\n                  <mml:mrow>\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:mo>⊂</mml:mo>\r\n                  <mml:msup>\r\n                    <mml:mrow>\r\n                      <mml:mi>R</mml:mi>\r\n                    </mml:mrow>\r\n                    <mml:mi>n</mml:mi>\r\n                  </mml:msup>\r\n                </mml:mrow>\r\n              </mml:math></jats:alternatives></jats:inline-formula>, <jats:inline-formula><jats:alternatives><jats:tex-math>$$n\\ge 2$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                <mml:mrow>\r\n                  <mml:mi>n</mml:mi>\r\n                  <mml:mo>≥</mml:mo>\r\n                  <mml:mn>2</mml:mn>\r\n                </mml:mrow>\r\n              </mml:math></jats:alternatives></jats:inline-formula>, the chemotaxis system <jats:disp-formula><jats:alternatives><jats:tex-math>$$\\begin{aligned} \\left\\{ \\begin{array}{l}u_t = \\nabla \\cdot \\big ( D(u) \\nabla u \\big ) - \\nabla \\cdot \\big ( uS(u)\\nabla v\\big ), \\\\ 0 = \\Delta v - \\mu + u, \\qquad \\mu =\\frac{1}{|\\Omega |} \\int _\\Omega u, \\end{array} \\right. \\qquad \\qquad (\\star ) \\end{aligned}$$</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:mrow>\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>u</mml:mi>\r\n                                        <mml:mi>t</mml:mi>\r\n                                      </mml:msub>\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:mo>(</mml:mo>\r\n                                      </mml:mrow>\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>∇</mml:mi>\r\n                                      <mml:mi>u</mml:mi>\r\n                                      <mml:mrow>\r\n                                        <mml:mo>)</mml:mo>\r\n                                      </mml:mrow>\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:mo>(</mml:mo>\r\n                                      </mml:mrow>\r\n                                      <mml:mi>u</mml:mi>\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>∇</mml:mi>\r\n                                      <mml:mi>v</mml:mi>\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: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:mspace />\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:msub>\r\n                                        <mml:mo>∫</mml:mo>\r\n                                        <mml:mi>Ω</mml:mi>\r\n                                      </mml:msub>\r\n                                      <mml:mi>u</mml:mi>\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:mspace />\r\n                          <mml:mspace />\r\n                          <mml:mrow>\r\n                            <mml:mo>(</mml:mo>\r\n                            <mml:mo>⋆</mml:mo>\r\n                            <mml:mo>)</mml:mo>\r\n                          </mml:mrow>\r\n                        </mml:mrow>\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>is considered under no-flux boundary conditions, with a focus on nonlinearities <jats:inline-formula><jats:alternatives><jats:tex-math>$$S\\in C^2([0,\\infty ))$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                <mml:mrow>\r\n                  <mml:mi>S</mml:mi>\r\n                  <mml:mo>∈</mml:mo>\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:mrow>\r\n                    <mml:mo>(</mml:mo>\r\n                    <mml:mrow>\r\n                      <mml:mo>[</mml:mo>\r\n                      <mml:mn>0</mml:mn>\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:mo>)</mml:mo>\r\n                  </mml:mrow>\r\n                </mml:mrow>\r\n              </mml:math></jats:alternatives></jats:inline-formula> which exhibit super-algebraically fast decay in the sense that with some <jats:inline-formula><jats:alternatives><jats:tex-math>$$K_S&gt;0, \\beta \\in [0,1)$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                <mml:mrow>\r\n                  <mml:msub>\r\n                    <mml:mi>K</mml:mi>\r\n                    <mml:mi>S</mml:mi>\r\n                  </mml:msub>\r\n                  <mml:mo>&gt;</mml:mo>\r\n                  <mml:mn>0</mml:mn>\r\n                  <mml:mo>,</mml:mo>\r\n                  <mml:mi>β</mml:mi>\r\n                  <mml:mo>∈</mml:mo>\r\n                  <mml:mrow>\r\n                    <mml:mo>[</mml:mo>\r\n                    <mml:mn>0</mml:mn>\r\n                    <mml:mo>,</mml:mo>\r\n                    <mml:mn>1</mml:mn>\r\n                    <mml:mo>)</mml:mo>\r\n                  </mml:mrow>\r\n                </mml:mrow>\r\n              </mml:math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\xi _0&gt;0$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                <mml:mrow>\r\n                  <mml:msub>\r\n                    <mml:mi>ξ</mml:mi>\r\n                    <mml:mn>0</mml:mn>\r\n                  </mml:msub>\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>, <jats:disp-formula><jats:alternatives><jats:tex-math>$$\\begin{aligned} S(\\xi )&gt;0 \\quad \\text{ and } \\quad S'(\\xi ) \\le -K_S\\xi ^{-\\beta } S(\\xi ) \\qquad \\text{ for } \\text{ all } \\xi \\ge \\xi _0. \\end{aligned}$$</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: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:mo>&gt;</mml:mo>\r\n                          <mml:mn>0</mml:mn>\r\n                          <mml:mspace />\r\n                          <mml:mspace />\r\n                          <mml:mtext>and</mml:mtext>\r\n                          <mml:mspace />\r\n                          <mml:mspace />\r\n                          <mml:msup>\r\n                            <mml:mi>S</mml:mi>\r\n                            <mml:mo>′</mml:mo>\r\n                          </mml:msup>\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:mo>-</mml:mo>\r\n                          <mml:msub>\r\n                            <mml:mi>K</mml:mi>\r\n                            <mml:mi>S</mml:mi>\r\n                          </mml:msub>\r\n                          <mml:msup>\r\n                            <mml:mi>ξ</mml:mi>\r\n                            <mml:mrow>\r\n                              <mml:mo>-</mml:mo>\r\n                              <mml:mi>β</mml:mi>\r\n                            </mml:mrow>\r\n                          </mml:msup>\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:mspace />\r\n                          <mml:mspace />\r\n                          <mml:mtext>for</mml:mtext>\r\n                          <mml:mspace />\r\n                          <mml:mspace />\r\n                          <mml:mtext>all</mml:mtext>\r\n                          <mml:mspace />\r\n                          <mml:mi>ξ</mml:mi>\r\n                          <mml:mo>≥</mml:mo>\r\n                          <mml:msub>\r\n                            <mml:mi>ξ</mml:mi>\r\n                            <mml:mn>0</mml:mn>\r\n                          </mml:msub>\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:math></jats:alternatives></jats:disp-formula>It is, inter alia, shown that if furthermore <jats:inline-formula><jats:alternatives><jats:tex-math>$$D\\in C^2((0,\\infty ))$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                <mml:mrow>\r\n                  <mml:mi>D</mml:mi>\r\n                  <mml:mo>∈</mml:mo>\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:mrow>\r\n                    <mml:mo>(</mml:mo>\r\n                    <mml:mrow>\r\n                      <mml:mo>(</mml:mo>\r\n                      <mml:mn>0</mml:mn>\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:mo>)</mml:mo>\r\n                  </mml:mrow>\r\n                </mml:mrow>\r\n              </mml:math></jats:alternatives></jats:inline-formula> is positive and suitably small in relation to <jats:italic>S</jats:italic> by satisfying <jats:disp-formula><jats:alternatives><jats:tex-math>$$\\begin{aligned} \\frac{\\xi S(\\xi )}{D(\\xi )} \\ge K_{SD}\\xi ^\\lambda \\qquad \\text{ for } \\text{ all } \\xi \\ge \\xi _0 \\end{aligned}$$</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:mrow>\r\n                          <mml:mfrac>\r\n                            <mml:mrow>\r\n                              <mml:mi>ξ</mml:mi>\r\n                              <mml:mi>S</mml:mi>\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:mi>D</mml:mi>\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:mfrac>\r\n                          <mml:mo>≥</mml:mo>\r\n                          <mml:msub>\r\n                            <mml:mi>K</mml:mi>\r\n                            <mml:mrow>\r\n                              <mml:mi>SD</mml:mi>\r\n                            </mml:mrow>\r\n                          </mml:msub>\r\n                          <mml:msup>\r\n                            <mml:mi>ξ</mml:mi>\r\n                            <mml:mi>λ</mml:mi>\r\n                          </mml:msup>\r\n                          <mml:mspace />\r\n                          <mml:mspace />\r\n                          <mml:mtext>for</mml:mtext>\r\n                          <mml:mspace />\r\n                          <mml:mspace />\r\n                          <mml:mtext>all</mml:mtext>\r\n                          <mml:mspace />\r\n                          <mml:mi>ξ</mml:mi>\r\n                          <mml:mo>≥</mml:mo>\r\n                          <mml:msub>\r\n                            <mml:mi>ξ</mml:mi>\r\n                            <mml:mn>0</mml:mn>\r\n                          </mml:msub>\r\n                        </mml:mrow>\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>with some <jats:inline-formula><jats:alternatives><jats:tex-math>$$K_{SD}&gt;0$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                <mml:mrow>\r\n                  <mml:msub>\r\n                    <mml:mi>K</mml:mi>\r\n                    <mml:mrow>\r\n                      <mml:mi>SD</mml:mi>\r\n                    </mml:mrow>\r\n                  </mml:msub>\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 <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\lambda &gt;\\frac{2}{n}$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                <mml:mrow>\r\n                  <mml:mi>λ</mml:mi>\r\n                  <mml:mo>&gt;</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:mrow>\r\n              </mml:math></jats:alternatives></jats:inline-formula>, then throughout a considerably large set of initial data, (<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\star $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                <mml:mo>⋆</mml:mo>\r\n              </mml:math></jats:alternatives></jats:inline-formula>) admits global classical solutions (<jats:italic>u</jats:italic>, <jats:italic>v</jats:italic>) fulfilling <jats:disp-formula><jats:alternatives><jats:tex-math>$$\\begin{aligned} \\frac{z(t)}{C} \\le \\Vert u(\\cdot ,t)\\Vert _{L^\\infty (\\Omega )} \\le Cz(t) \\qquad \\text{ for } \\text{ all } t&gt;0, \\end{aligned}$$</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:mrow>\r\n                          <mml:mfrac>\r\n                            <mml:mrow>\r\n                              <mml:mi>z</mml:mi>\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:mi>C</mml:mi>\r\n                          </mml:mfrac>\r\n                          <mml:mo>≤</mml:mo>\r\n                          <mml:msub>\r\n                            <mml:mrow>\r\n                              <mml:mo>‖</mml:mo>\r\n                              <mml:mi>u</mml:mi>\r\n                              <mml:mrow>\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: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:mrow>\r\n                          </mml:msub>\r\n                          <mml:mo>≤</mml:mo>\r\n                          <mml:mi>C</mml:mi>\r\n                          <mml:mi>z</mml:mi>\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:mrow>\r\n                          <mml:mspace />\r\n                          <mml:mspace />\r\n                          <mml:mtext>for</mml:mtext>\r\n                          <mml:mspace />\r\n                          <mml:mspace />\r\n                          <mml:mtext>all</mml:mtext>\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: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:math></jats:alternatives></jats:disp-formula>with some <jats:inline-formula><jats:alternatives><jats:tex-math>$$C=C^{(u,v)}\\ge 1$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                <mml:mrow>\r\n                  <mml:mi>C</mml:mi>\r\n                  <mml:mo>=</mml:mo>\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>u</mml:mi>\r\n                      <mml:mo>,</mml:mo>\r\n                      <mml:mi>v</mml:mi>\r\n                      <mml:mo>)</mml:mo>\r\n                    </mml:mrow>\r\n                  </mml:msup>\r\n                  <mml:mo>≥</mml:mo>\r\n                  <mml:mn>1</mml:mn>\r\n                </mml:mrow>\r\n              </mml:math></jats:alternatives></jats:inline-formula>, where <jats:italic>z</jats:italic> denotes the solution of <jats:disp-formula><jats:alternatives><jats:tex-math>$$\\begin{aligned} \\left\\{ \\begin{array}{l}z'(t) = z^2(t) \\cdot S\\big ( z(t)\\big ), \\qquad t&gt;0, \\\\ z(0)=\\xi _0, \\end{array} \\right. \\end{aligned}$$</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:msup>\r\n                                      <mml:mi>z</mml:mi>\r\n                                      <mml:mo>′</mml:mo>\r\n                                    </mml:msup>\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:mrow>\r\n                                    <mml:mo>=</mml:mo>\r\n                                    <mml:msup>\r\n                                      <mml:mi>z</mml:mi>\r\n                                      <mml:mn>2</mml:mn>\r\n                                    </mml:msup>\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: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:mrow>\r\n                                    <mml:mi>z</mml:mi>\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:mrow>\r\n                                    <mml:mrow>\r\n                                      <mml:mo>)</mml:mo>\r\n                                    </mml:mrow>\r\n                                    <mml:mo>,</mml:mo>\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: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:mi>z</mml:mi>\r\n                                    <mml:mrow>\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:mo>=</mml:mo>\r\n                                    <mml:msub>\r\n                                      <mml:mi>ξ</mml:mi>\r\n                                      <mml:mn>0</mml:mn>\r\n                                    </mml:msub>\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>which is seen to exist globally, and to satisfy <jats:inline-formula><jats:alternatives><jats:tex-math>$$z(t)\\rightarrow +\\infty $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                <mml:mrow>\r\n                  <mml:mi>z</mml:mi>\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:mo>+</mml:mo>\r\n                  <mml:mi>∞</mml:mi>\r\n                </mml:mrow>\r\n              </mml:math></jats:alternatives></jats:inline-formula> as <jats:inline-formula><jats:alternatives><jats:tex-math>$$t\\rightarrow \\infty $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                <mml:mrow>\r\n                  <mml:mi>t</mml:mi>\r\n                  <mml:mo>→</mml:mo>\r\n                  <mml:mi>∞</mml:mi>\r\n                </mml:mrow>\r\n              </mml:math></jats:alternatives></jats:inline-formula>. As particular examples, exponentially and doubly exponentially decaying <jats:italic>S</jats:italic> are found to imply corresponding infinite-time blow-up properties in (<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\star $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                <mml:mo>⋆</mml:mo>\r\n              </mml:math></jats:alternatives></jats:inline-formula>) at logarithmic and doubly logarithmic rates, respectively.</jats:p>","lang":"eng"}],"publication":"Journal of Dynamics and Differential Equations","type":"journal_article","language":[{"iso":"eng"}],"keyword":["Analysis"],"user_id":"31496","_id":"53323"},{"page":"390-418","intvolume":"       343","citation":{"chicago":"Tao, Youshan, and Michael Winkler. “Global Solutions to a Keller-Segel-Consumption System Involving Singularly Signal-Dependent Motilities in Domains of Arbitrary Dimension.” <i>Journal of Differential Equations</i> 343 (2022): 390–418. <a href=\"https://doi.org/10.1016/j.jde.2022.10.022\">https://doi.org/10.1016/j.jde.2022.10.022</a>.","ieee":"Y. Tao and M. Winkler, “Global solutions to a Keller-Segel-consumption system involving singularly signal-dependent motilities in domains of arbitrary dimension,” <i>Journal of Differential Equations</i>, vol. 343, pp. 390–418, 2022, doi: <a href=\"https://doi.org/10.1016/j.jde.2022.10.022\">10.1016/j.jde.2022.10.022</a>.","ama":"Tao Y, Winkler M. Global solutions to a Keller-Segel-consumption system involving singularly signal-dependent motilities in domains of arbitrary dimension. <i>Journal of Differential Equations</i>. 2022;343:390-418. doi:<a href=\"https://doi.org/10.1016/j.jde.2022.10.022\">10.1016/j.jde.2022.10.022</a>","bibtex":"@article{Tao_Winkler_2022, title={Global solutions to a Keller-Segel-consumption system involving singularly signal-dependent motilities in domains of arbitrary dimension}, volume={343}, DOI={<a href=\"https://doi.org/10.1016/j.jde.2022.10.022\">10.1016/j.jde.2022.10.022</a>}, journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Tao, Youshan and Winkler, Michael}, year={2022}, pages={390–418} }","short":"Y. Tao, M. Winkler, Journal of Differential Equations 343 (2022) 390–418.","mla":"Tao, Youshan, and Michael Winkler. “Global Solutions to a Keller-Segel-Consumption System Involving Singularly Signal-Dependent Motilities in Domains of Arbitrary Dimension.” <i>Journal of Differential Equations</i>, vol. 343, Elsevier BV, 2022, pp. 390–418, doi:<a href=\"https://doi.org/10.1016/j.jde.2022.10.022\">10.1016/j.jde.2022.10.022</a>.","apa":"Tao, Y., &#38; Winkler, M. (2022). Global solutions to a Keller-Segel-consumption system involving singularly signal-dependent motilities in domains of arbitrary dimension. <i>Journal of Differential Equations</i>, <i>343</i>, 390–418. <a href=\"https://doi.org/10.1016/j.jde.2022.10.022\">https://doi.org/10.1016/j.jde.2022.10.022</a>"},"year":"2022","publication_identifier":{"issn":["0022-0396"]},"publication_status":"published","doi":"10.1016/j.jde.2022.10.022","title":"Global solutions to a Keller-Segel-consumption system involving singularly signal-dependent motilities in domains of arbitrary dimension","volume":343,"author":[{"first_name":"Youshan","full_name":"Tao, Youshan","last_name":"Tao"},{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"date_created":"2024-04-07T12:42:28Z","date_updated":"2024-04-07T12:42:32Z","publisher":"Elsevier BV","status":"public","publication":"Journal of Differential Equations","type":"journal_article","language":[{"iso":"eng"}],"keyword":["Analysis","Applied Mathematics"],"user_id":"31496","_id":"53327"},{"status":"public","type":"journal_article","publication":"Nonlinear Analysis","language":[{"iso":"eng"}],"article_number":"113153","keyword":["Applied Mathematics","Analysis"],"user_id":"31496","_id":"53325","citation":{"ieee":"L. Desvillettes, P. Laurençot, A. Trescases, and M. Winkler, “Weak solutions to triangular cross diffusion systems modeling chemotaxis with local sensing,” <i>Nonlinear Analysis</i>, vol. 226, Art. no. 113153, 2022, doi: <a href=\"https://doi.org/10.1016/j.na.2022.113153\">10.1016/j.na.2022.113153</a>.","chicago":"Desvillettes, Laurent, Philippe Laurençot, Ariane Trescases, and Michael Winkler. “Weak Solutions to Triangular Cross Diffusion Systems Modeling Chemotaxis with Local Sensing.” <i>Nonlinear Analysis</i> 226 (2022). <a href=\"https://doi.org/10.1016/j.na.2022.113153\">https://doi.org/10.1016/j.na.2022.113153</a>.","ama":"Desvillettes L, Laurençot P, Trescases A, Winkler M. Weak solutions to triangular cross diffusion systems modeling chemotaxis with local sensing. <i>Nonlinear Analysis</i>. 2022;226. doi:<a href=\"https://doi.org/10.1016/j.na.2022.113153\">10.1016/j.na.2022.113153</a>","bibtex":"@article{Desvillettes_Laurençot_Trescases_Winkler_2022, title={Weak solutions to triangular cross diffusion systems modeling chemotaxis with local sensing}, volume={226}, DOI={<a href=\"https://doi.org/10.1016/j.na.2022.113153\">10.1016/j.na.2022.113153</a>}, number={113153}, journal={Nonlinear Analysis}, publisher={Elsevier BV}, author={Desvillettes, Laurent and Laurençot, Philippe and Trescases, Ariane and Winkler, Michael}, year={2022} }","mla":"Desvillettes, Laurent, et al. “Weak Solutions to Triangular Cross Diffusion Systems Modeling Chemotaxis with Local Sensing.” <i>Nonlinear Analysis</i>, vol. 226, 113153, Elsevier BV, 2022, doi:<a href=\"https://doi.org/10.1016/j.na.2022.113153\">10.1016/j.na.2022.113153</a>.","short":"L. Desvillettes, P. Laurençot, A. Trescases, M. Winkler, Nonlinear Analysis 226 (2022).","apa":"Desvillettes, L., Laurençot, P., Trescases, A., &#38; Winkler, M. (2022). Weak solutions to triangular cross diffusion systems modeling chemotaxis with local sensing. <i>Nonlinear Analysis</i>, <i>226</i>, Article 113153. <a href=\"https://doi.org/10.1016/j.na.2022.113153\">https://doi.org/10.1016/j.na.2022.113153</a>"},"intvolume":"       226","year":"2022","publication_status":"published","publication_identifier":{"issn":["0362-546X"]},"doi":"10.1016/j.na.2022.113153","title":"Weak solutions to triangular cross diffusion systems modeling chemotaxis with local sensing","date_created":"2024-04-07T12:41:15Z","author":[{"first_name":"Laurent","full_name":"Desvillettes, Laurent","last_name":"Desvillettes"},{"first_name":"Philippe","last_name":"Laurençot","full_name":"Laurençot, Philippe"},{"first_name":"Ariane","full_name":"Trescases, Ariane","last_name":"Trescases"},{"last_name":"Winkler","full_name":"Winkler, Michael","first_name":"Michael"}],"volume":226,"publisher":"Elsevier BV","date_updated":"2024-04-07T12:41:20Z"},{"title":"Finite-time blow-up in a repulsive chemotaxis-consumption system","doi":"10.1017/prm.2022.39","publisher":"Cambridge University Press (CUP)","date_updated":"2024-04-07T12:44:30Z","date_created":"2024-04-07T12:44:26Z","author":[{"first_name":"Yulan","last_name":"Wang","full_name":"Wang, Yulan"},{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"volume":153,"year":"2022","citation":{"short":"Y. Wang, M. Winkler, Proceedings of the Royal Society of Edinburgh: Section A Mathematics 153 (2022) 1150–1166.","mla":"Wang, Yulan, and Michael Winkler. “Finite-Time Blow-up in a Repulsive Chemotaxis-Consumption System.” <i>Proceedings of the Royal Society of Edinburgh: Section A Mathematics</i>, vol. 153, no. 4, Cambridge University Press (CUP), 2022, pp. 1150–66, doi:<a href=\"https://doi.org/10.1017/prm.2022.39\">10.1017/prm.2022.39</a>.","bibtex":"@article{Wang_Winkler_2022, title={Finite-time blow-up in a repulsive chemotaxis-consumption system}, volume={153}, DOI={<a href=\"https://doi.org/10.1017/prm.2022.39\">10.1017/prm.2022.39</a>}, number={4}, journal={Proceedings of the Royal Society of Edinburgh: Section A Mathematics}, publisher={Cambridge University Press (CUP)}, author={Wang, Yulan and Winkler, Michael}, year={2022}, pages={1150–1166} }","apa":"Wang, Y., &#38; Winkler, M. (2022). Finite-time blow-up in a repulsive chemotaxis-consumption system. <i>Proceedings of the Royal Society of Edinburgh: Section A Mathematics</i>, <i>153</i>(4), 1150–1166. <a href=\"https://doi.org/10.1017/prm.2022.39\">https://doi.org/10.1017/prm.2022.39</a>","ieee":"Y. Wang and M. Winkler, “Finite-time blow-up in a repulsive chemotaxis-consumption system,” <i>Proceedings of the Royal Society of Edinburgh: Section A Mathematics</i>, vol. 153, no. 4, pp. 1150–1166, 2022, doi: <a href=\"https://doi.org/10.1017/prm.2022.39\">10.1017/prm.2022.39</a>.","chicago":"Wang, Yulan, and Michael Winkler. “Finite-Time Blow-up in a Repulsive Chemotaxis-Consumption System.” <i>Proceedings of the Royal Society of Edinburgh: Section A Mathematics</i> 153, no. 4 (2022): 1150–66. <a href=\"https://doi.org/10.1017/prm.2022.39\">https://doi.org/10.1017/prm.2022.39</a>.","ama":"Wang Y, Winkler M. Finite-time blow-up in a repulsive chemotaxis-consumption system. <i>Proceedings of the Royal Society of Edinburgh: Section A Mathematics</i>. 2022;153(4):1150-1166. doi:<a href=\"https://doi.org/10.1017/prm.2022.39\">10.1017/prm.2022.39</a>"},"page":"1150-1166","intvolume":"       153","publication_status":"published","publication_identifier":{"issn":["0308-2105","1473-7124"]},"issue":"4","keyword":["General Mathematics"],"language":[{"iso":"eng"}],"_id":"53331","user_id":"31496","abstract":[{"lang":"eng","text":"<jats:p>In a ball <jats:inline-formula><jats:alternatives><jats:tex-math>$\\Omega \\subset \\mathbb {R}^{n}$</jats:tex-math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0308210522000397_inline1.png\" /></jats:alternatives></jats:inline-formula> with <jats:inline-formula><jats:alternatives><jats:tex-math>$n\\ge 2$</jats:tex-math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0308210522000397_inline2.png\" /></jats:alternatives></jats:inline-formula>, the chemotaxis system\r\n<jats:disp-formula><jats:alternatives><jats:tex-math>\\[ \\left\\{ \\begin{array}{@{}l} u_t = \\nabla \\cdot \\big( D(u)\\nabla u\\big) + \\nabla\\cdot \\big(\\dfrac{u}{v} \\nabla v\\big), \\\\ 0=\\Delta v - uv \\end{array} \\right. \\]</jats:tex-math><jats:graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" mimetype=\"image\" position=\"float\" xlink:href=\"S0308210522000397_eqnU1.png\" /></jats:alternatives></jats:disp-formula>is considered along with no-flux boundary conditions for <jats:inline-formula><jats:alternatives><jats:tex-math>$u$</jats:tex-math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0308210522000397_inline3.png\" /></jats:alternatives></jats:inline-formula> and with prescribed constant positive Dirichlet boundary data for <jats:inline-formula><jats:alternatives><jats:tex-math>$v$</jats:tex-math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0308210522000397_inline4.png\" /></jats:alternatives></jats:inline-formula>. It is shown that if <jats:inline-formula><jats:alternatives><jats:tex-math>$D\\in C^{3}([0,\\infty ))$</jats:tex-math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0308210522000397_inline5.png\" /></jats:alternatives></jats:inline-formula> is such that <jats:inline-formula><jats:alternatives><jats:tex-math>$0&lt; D(\\xi ) \\le {K_D} (\\xi +1)^{-\\alpha }$</jats:tex-math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0308210522000397_inline6.png\" /></jats:alternatives></jats:inline-formula> for all <jats:inline-formula><jats:alternatives><jats:tex-math>$\\xi &gt;0$</jats:tex-math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0308210522000397_inline7.png\" /></jats:alternatives></jats:inline-formula> with some <jats:inline-formula><jats:alternatives><jats:tex-math>${K_D}&gt;0$</jats:tex-math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0308210522000397_inline8.png\" /></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$\\alpha &gt;0$</jats:tex-math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0308210522000397_inline9.png\" /></jats:alternatives></jats:inline-formula>, then for all initial data from a considerably large set of radial functions on <jats:inline-formula><jats:alternatives><jats:tex-math>$\\Omega$</jats:tex-math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0308210522000397_inline10.png\" /></jats:alternatives></jats:inline-formula>, the corresponding initial-boundary value problem admits a solution blowing up in finite time.</jats:p>"}],"status":"public","type":"journal_article","publication":"Proceedings of the Royal Society of Edinburgh: Section A Mathematics"},{"publisher":"World Scientific Pub Co Pte Ltd","date_updated":"2024-04-07T12:55:11Z","author":[{"first_name":"Michael","full_name":"Winkler, Michael","last_name":"Winkler"}],"date_created":"2024-04-07T12:55:07Z","volume":13,"title":"Application of the Moser–Trudinger inequality in the construction of global solutions to a strongly degenerate migration model","doi":"10.1142/s1664360722500126","publication_status":"published","publication_identifier":{"issn":["1664-3607","1664-3615"]},"issue":"02","year":"2022","citation":{"ama":"Winkler M. Application of the Moser–Trudinger inequality in the construction of global solutions to a strongly degenerate migration model. <i>Bulletin of Mathematical Sciences</i>. 2022;13(02). doi:<a href=\"https://doi.org/10.1142/s1664360722500126\">10.1142/s1664360722500126</a>","ieee":"M. Winkler, “Application of the Moser–Trudinger inequality in the construction of global solutions to a strongly degenerate migration model,” <i>Bulletin of Mathematical Sciences</i>, vol. 13, no. 02, 2022, doi: <a href=\"https://doi.org/10.1142/s1664360722500126\">10.1142/s1664360722500126</a>.","chicago":"Winkler, Michael. “Application of the Moser–Trudinger Inequality in the Construction of Global Solutions to a Strongly Degenerate Migration Model.” <i>Bulletin of Mathematical Sciences</i> 13, no. 02 (2022). <a href=\"https://doi.org/10.1142/s1664360722500126\">https://doi.org/10.1142/s1664360722500126</a>.","apa":"Winkler, M. (2022). Application of the Moser–Trudinger inequality in the construction of global solutions to a strongly degenerate migration model. <i>Bulletin of Mathematical Sciences</i>, <i>13</i>(02). <a href=\"https://doi.org/10.1142/s1664360722500126\">https://doi.org/10.1142/s1664360722500126</a>","short":"M. Winkler, Bulletin of Mathematical Sciences 13 (2022).","mla":"Winkler, Michael. “Application of the Moser–Trudinger Inequality in the Construction of Global Solutions to a Strongly Degenerate Migration Model.” <i>Bulletin of Mathematical Sciences</i>, vol. 13, no. 02, World Scientific Pub Co Pte Ltd, 2022, doi:<a href=\"https://doi.org/10.1142/s1664360722500126\">10.1142/s1664360722500126</a>.","bibtex":"@article{Winkler_2022, title={Application of the Moser–Trudinger inequality in the construction of global solutions to a strongly degenerate migration model}, volume={13}, DOI={<a href=\"https://doi.org/10.1142/s1664360722500126\">10.1142/s1664360722500126</a>}, number={02}, journal={Bulletin of Mathematical Sciences}, publisher={World Scientific Pub Co Pte Ltd}, author={Winkler, Michael}, year={2022} }"},"intvolume":"        13","_id":"53344","user_id":"31496","keyword":["General Mathematics"],"language":[{"iso":"eng"}],"type":"journal_article","publication":"Bulletin of Mathematical Sciences","abstract":[{"lang":"eng","text":"<jats:p> A no-flux initial-boundary value problem for the cross-diffusion system [Formula: see text] is considered in smoothly bounded domains [Formula: see text] with [Formula: see text]. It is shown that whenever [Formula: see text] is positive on [Formula: see text] and such that [Formula: see text] for some [Formula: see text], for all suitably regular positive initial data a global very weak solution, particularly preserving mass in its first component, can be constructed. This extends previous results which either concentrate on non-degenerate analogs, or are restricted to the special case [Formula: see text]. </jats:p><jats:p> To appropriately cope with the considerably stronger cross-degeneracies thus allowed through [Formula: see text] when [Formula: see text] is large, in its core part the analysis relies on the use of the Moser–Trudinger inequality in controlling the respective diffusion rates [Formula: see text] from below. </jats:p>"}],"status":"public"},{"title":"Zusatzkosten der Besteuerung – Eine Analyse des steuerlichen Verwaltungsaufwands und der subjektiv wahrgenommenen Steuerbelastung (An Empirical Analysis of Firms’ Hidden Cost of Taxation)","main_file_link":[{"open_access":"1"}],"doi":"10.2139/ssrn.4210460","oa":"1","date_updated":"2024-04-08T11:33:02Z","author":[{"first_name":"Martin","last_name":"Fochmann","full_name":"Fochmann, Martin"},{"id":"83380","full_name":"Heinemann-Heile, Vanessa","last_name":"Heinemann-Heile","first_name":"Vanessa"},{"last_name":"Huber","full_name":"Huber, Hans-Peter","first_name":"Hans-Peter"},{"first_name":"Ralf","last_name":"Maiterth","full_name":"Maiterth, Ralf"},{"id":"530","full_name":"Sureth-Sloane, Caren","last_name":"Sureth-Sloane","orcid":" 0000-0002-8183-5901","first_name":"Caren"}],"date_created":"2023-01-10T10:51:40Z","volume":100,"year":"2022","citation":{"bibtex":"@book{Fochmann_Heinemann-Heile_Huber_Maiterth_Sureth-Sloane_2022, series={TRR 266 Accounting for Transparency Working Paper Series}, title={Zusatzkosten der Besteuerung – Eine Analyse des steuerlichen Verwaltungsaufwands und der subjektiv wahrgenommenen Steuerbelastung (An Empirical Analysis of Firms’ Hidden Cost of Taxation)}, volume={100}, DOI={<a href=\"https://doi.org/10.2139/ssrn.4210460\">10.2139/ssrn.4210460</a>}, author={Fochmann, Martin and Heinemann-Heile, Vanessa and Huber, Hans-Peter and Maiterth, Ralf and Sureth-Sloane, Caren}, year={2022}, collection={TRR 266 Accounting for Transparency Working Paper Series} }","mla":"Fochmann, Martin, et al. <i>Zusatzkosten der Besteuerung – Eine Analyse des steuerlichen Verwaltungsaufwands und der subjektiv wahrgenommenen Steuerbelastung (An Empirical Analysis of Firms’ Hidden Cost of Taxation)</i>. 2022, doi:<a href=\"https://doi.org/10.2139/ssrn.4210460\">10.2139/ssrn.4210460</a>.","short":"M. Fochmann, V. Heinemann-Heile, H.-P. Huber, R. Maiterth, C. Sureth-Sloane, Zusatzkosten der Besteuerung – Eine Analyse des steuerlichen Verwaltungsaufwands und der subjektiv wahrgenommenen Steuerbelastung (An Empirical Analysis of Firms’ Hidden Cost of Taxation), 2022.","apa":"Fochmann, M., Heinemann-Heile, V., Huber, H.-P., Maiterth, R., &#38; Sureth-Sloane, C. (2022). <i>Zusatzkosten der Besteuerung – Eine Analyse des steuerlichen Verwaltungsaufwands und der subjektiv wahrgenommenen Steuerbelastung (An Empirical Analysis of Firms’ Hidden Cost of Taxation)</i> (Vol. 100). <a href=\"https://doi.org/10.2139/ssrn.4210460\">https://doi.org/10.2139/ssrn.4210460</a>","ama":"Fochmann M, Heinemann-Heile V, Huber H-P, Maiterth R, Sureth-Sloane C. <i>Zusatzkosten der Besteuerung – Eine Analyse des steuerlichen Verwaltungsaufwands und der subjektiv wahrgenommenen Steuerbelastung (An Empirical Analysis of Firms’ Hidden Cost of Taxation)</i>. Vol 100.; 2022. doi:<a href=\"https://doi.org/10.2139/ssrn.4210460\">10.2139/ssrn.4210460</a>","chicago":"Fochmann, Martin, Vanessa Heinemann-Heile, Hans-Peter Huber, Ralf Maiterth, and Caren Sureth-Sloane. <i>Zusatzkosten der Besteuerung – Eine Analyse des steuerlichen Verwaltungsaufwands und der subjektiv wahrgenommenen Steuerbelastung (An Empirical Analysis of Firms’ Hidden Cost of Taxation)</i>. Vol. 100. TRR 266 Accounting for Transparency Working Paper Series, 2022. <a href=\"https://doi.org/10.2139/ssrn.4210460\">https://doi.org/10.2139/ssrn.4210460</a>.","ieee":"M. Fochmann, V. Heinemann-Heile, H.-P. Huber, R. Maiterth, and C. Sureth-Sloane, <i>Zusatzkosten der Besteuerung – Eine Analyse des steuerlichen Verwaltungsaufwands und der subjektiv wahrgenommenen Steuerbelastung (An Empirical Analysis of Firms’ Hidden Cost of Taxation)</i>, vol. 100. 2022."},"intvolume":"       100","publication_status":"published","publication_identifier":{"issn":["1556-5068"]},"keyword":["General Earth and Planetary Sciences","General Environmental Science"],"language":[{"iso":"ger"}],"_id":"35788","series_title":"TRR 266 Accounting for Transparency Working Paper Series","user_id":"530","department":[{"_id":"187"}],"status":"public","type":"working_paper"},{"title":"Towards an Amended Arm's Length Principle - Tackling complexity and implementing destination rules in transfer pricing","doi":"10.2139/ssrn.4166972","main_file_link":[{"open_access":"1"}],"oa":"1","date_updated":"2024-04-08T11:32:32Z","volume":89,"date_created":"2023-01-10T11:00:37Z","author":[{"last_name":"Greil","full_name":"Greil, Stefan","first_name":"Stefan"},{"first_name":"Michael","last_name":"Overesch","full_name":"Overesch, Michael"},{"last_name":"Rohlfing-Bastian","full_name":"Rohlfing-Bastian, Anna","first_name":"Anna"},{"first_name":"Ulrich","last_name":"Schreiber","full_name":"Schreiber, Ulrich"},{"id":"530","full_name":"Sureth-Sloane, Caren","last_name":"Sureth-Sloane","orcid":" 0000-0002-8183-5901","first_name":"Caren"}],"year":"2022","intvolume":"        89","citation":{"apa":"Greil, S., Overesch, M., Rohlfing-Bastian, A., Schreiber, U., &#38; Sureth-Sloane, C. (2022). <i>Towards an Amended Arm’s Length Principle - Tackling complexity and implementing destination rules in transfer pricing</i> (Vol. 89). <a href=\"https://doi.org/10.2139/ssrn.4166972\">https://doi.org/10.2139/ssrn.4166972</a>","short":"S. Greil, M. Overesch, A. Rohlfing-Bastian, U. Schreiber, C. Sureth-Sloane, Towards an Amended Arm’s Length Principle - Tackling Complexity and Implementing Destination Rules in Transfer Pricing, 2022.","mla":"Greil, Stefan, et al. <i>Towards an Amended Arm’s Length Principle - Tackling Complexity and Implementing Destination Rules in Transfer Pricing</i>. 2022, doi:<a href=\"https://doi.org/10.2139/ssrn.4166972\">10.2139/ssrn.4166972</a>.","bibtex":"@book{Greil_Overesch_Rohlfing-Bastian_Schreiber_Sureth-Sloane_2022, series={TRR 266 Accounting for Transparency Working Paper Series}, title={Towards an Amended Arm’s Length Principle - Tackling complexity and implementing destination rules in transfer pricing}, volume={89}, DOI={<a href=\"https://doi.org/10.2139/ssrn.4166972\">10.2139/ssrn.4166972</a>}, author={Greil, Stefan and Overesch, Michael and Rohlfing-Bastian, Anna and Schreiber, Ulrich and Sureth-Sloane, Caren}, year={2022}, collection={TRR 266 Accounting for Transparency Working Paper Series} }","ieee":"S. Greil, M. Overesch, A. Rohlfing-Bastian, U. Schreiber, and C. Sureth-Sloane, <i>Towards an Amended Arm’s Length Principle - Tackling complexity and implementing destination rules in transfer pricing</i>, vol. 89. 2022.","chicago":"Greil, Stefan, Michael Overesch, Anna Rohlfing-Bastian, Ulrich Schreiber, and Caren Sureth-Sloane. <i>Towards an Amended Arm’s Length Principle - Tackling Complexity and Implementing Destination Rules in Transfer Pricing</i>. Vol. 89. TRR 266 Accounting for Transparency Working Paper Series, 2022. <a href=\"https://doi.org/10.2139/ssrn.4166972\">https://doi.org/10.2139/ssrn.4166972</a>.","ama":"Greil S, Overesch M, Rohlfing-Bastian A, Schreiber U, Sureth-Sloane C. <i>Towards an Amended Arm’s Length Principle - Tackling Complexity and Implementing Destination Rules in Transfer Pricing</i>. Vol 89.; 2022. doi:<a href=\"https://doi.org/10.2139/ssrn.4166972\">10.2139/ssrn.4166972</a>"},"publication_identifier":{"issn":["1556-5068"]},"publication_status":"published","language":[{"iso":"eng"}],"_id":"35795","department":[{"_id":"187"}],"user_id":"530","series_title":"TRR 266 Accounting for Transparency Working Paper Series","status":"public","type":"working_paper"},{"publication_status":"published","place":"Münster","year":"2022","citation":{"ieee":"G. Werth, “Neue Wege im mathematischen Unterricht - Auf den Spuren Mathilde Vaertings,” presented at the 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik, Frankfurt am. Main, 2022, doi: <a href=\"https://doi.org/10.37626/GA9783959872089.0\">https://doi.org/10.37626/GA9783959872089.0</a>.","chicago":"Werth, Gerda. “Neue Wege im mathematischen Unterricht - Auf den Spuren Mathilde Vaertings.” In <i>Beiträge zum Mathematikunterricht</i>. Münster: WTM, 2022. <a href=\"https://doi.org/10.37626/GA9783959872089.0\">https://doi.org/10.37626/GA9783959872089.0</a>.","ama":"Werth G. Neue Wege im mathematischen Unterricht - Auf den Spuren Mathilde Vaertings. In: <i>Beiträge zum Mathematikunterricht</i>. WTM; 2022. doi:<a href=\"https://doi.org/10.37626/GA9783959872089.0\">https://doi.org/10.37626/GA9783959872089.0</a>","short":"G. Werth, in: Beiträge zum Mathematikunterricht, WTM, Münster, 2022.","mla":"Werth, Gerda. “Neue Wege im mathematischen Unterricht - Auf den Spuren Mathilde Vaertings.” <i>Beiträge zum Mathematikunterricht</i>, WTM, 2022, doi:<a href=\"https://doi.org/10.37626/GA9783959872089.0\">https://doi.org/10.37626/GA9783959872089.0</a>.","bibtex":"@inproceedings{Werth_2022, place={Münster}, title={Neue Wege im mathematischen Unterricht - Auf den Spuren Mathilde Vaertings}, DOI={<a href=\"https://doi.org/10.37626/GA9783959872089.0\">https://doi.org/10.37626/GA9783959872089.0</a>}, booktitle={Beiträge zum Mathematikunterricht}, publisher={WTM}, author={Werth, Gerda}, year={2022} }","apa":"Werth, G. (2022). Neue Wege im mathematischen Unterricht - Auf den Spuren Mathilde Vaertings. <i>Beiträge zum Mathematikunterricht</i>. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik, Frankfurt am. Main. <a href=\"https://doi.org/10.37626/GA9783959872089.0\">https://doi.org/10.37626/GA9783959872089.0</a>"},"date_updated":"2024-04-09T10:56:58Z","publisher":"WTM","date_created":"2024-03-14T11:17:56Z","author":[{"full_name":"Werth, Gerda","id":"578","last_name":"Werth","first_name":"Gerda"}],"title":"Neue Wege im mathematischen Unterricht - Auf den Spuren Mathilde Vaertings","doi":"https://doi.org/10.37626/GA9783959872089.0","conference":{"end_date":"2022-09-02","location":"Frankfurt am. Main","name":"56. Jahrestagung der Gesellschaft für Didaktik der Mathematik","start_date":"2022-08-29"},"publication":"Beiträge zum Mathematikunterricht","type":"conference","status":"public","_id":"52574","department":[{"_id":"10"},{"_id":"98"},{"_id":"360"}],"user_id":"578","language":[{"iso":"ger"}]},{"intvolume":"        31","page":"824-829","citation":{"ama":"Arbeitskreis Verrechnungspreise der Schmalenbach-Gesellschaft für Betriebswirtschaftslehre e.V. ., lead authors: Kreuzer A, Maier H, et al. Chancen und Risiken eines Cooperative Compliance-Ansatzes für die deutsche Besteuerungspraxis von multinationalen Unternehmen – Erfahrungen verschiedener Länder und Eindrücke deutscher Unternehmensvertreter. <i>Internationales Steuerrecht</i>. 2022;31(22):824-829.","ieee":". Arbeitskreis Verrechnungspreise der Schmalenbach-Gesellschaft für Betriebswirtschaftslehre e.V. <i>et al.</i>, “Chancen und Risiken eines Cooperative Compliance-Ansatzes für die deutsche Besteuerungspraxis von multinationalen Unternehmen – Erfahrungen verschiedener Länder und Eindrücke deutscher Unternehmensvertreter,” <i>Internationales Steuerrecht</i>, vol. 31, no. 22, pp. 824–829, 2022.","chicago":"Arbeitskreis Verrechnungspreise der Schmalenbach-Gesellschaft für Betriebswirtschaftslehre e.V., ., A lead authors: Kreuzer, H Maier, J. T. Martini, Rainer Niemann, Maite Schachtebeck, Dirk Simons, J Stoltenberg, and Caren Sureth-Sloane. “Chancen und Risiken eines Cooperative Compliance-Ansatzes für die deutsche Besteuerungspraxis von multinationalen Unternehmen – Erfahrungen verschiedener Länder und Eindrücke deutscher Unternehmensvertreter.” <i>Internationales Steuerrecht</i> 31, no. 22 (2022): 824–29.","apa":"Arbeitskreis Verrechnungspreise der Schmalenbach-Gesellschaft für Betriebswirtschaftslehre e.V., ., lead authors: Kreuzer, A., Maier, H., Martini, J. T., Niemann, R., Schachtebeck, M., Simons, D., Stoltenberg, J., &#38; Sureth-Sloane, C. (2022). Chancen und Risiken eines Cooperative Compliance-Ansatzes für die deutsche Besteuerungspraxis von multinationalen Unternehmen – Erfahrungen verschiedener Länder und Eindrücke deutscher Unternehmensvertreter. <i>Internationales Steuerrecht</i>, <i>31</i>(22), 824–829.","mla":"Arbeitskreis Verrechnungspreise der Schmalenbach-Gesellschaft für Betriebswirtschaftslehre e.V., ., et al. “Chancen und Risiken eines Cooperative Compliance-Ansatzes für die deutsche Besteuerungspraxis von multinationalen Unternehmen – Erfahrungen verschiedener Länder und Eindrücke deutscher Unternehmensvertreter.” <i>Internationales Steuerrecht</i>, vol. 31, no. 22, 2022, pp. 824–29.","short":". Arbeitskreis Verrechnungspreise der Schmalenbach-Gesellschaft für Betriebswirtschaftslehre e.V., A. lead authors: Kreuzer, H. Maier, J.T. Martini, R. Niemann, M. Schachtebeck, D. Simons, J. Stoltenberg, C. Sureth-Sloane, Internationales Steuerrecht 31 (2022) 824–829.","bibtex":"@article{Arbeitskreis Verrechnungspreise der Schmalenbach-Gesellschaft für Betriebswirtschaftslehre e.V._lead authors: Kreuzer_Maier_Martini_Niemann_Schachtebeck_Simons_Stoltenberg_Sureth-Sloane_2022, title={Chancen und Risiken eines Cooperative Compliance-Ansatzes für die deutsche Besteuerungspraxis von multinationalen Unternehmen – Erfahrungen verschiedener Länder und Eindrücke deutscher Unternehmensvertreter}, volume={31}, number={22}, journal={Internationales Steuerrecht}, author={Arbeitskreis Verrechnungspreise der Schmalenbach-Gesellschaft für Betriebswirtschaftslehre e.V., . and lead authors: Kreuzer, A and Maier, H and Martini, J. T. and Niemann, Rainer and Schachtebeck, Maite and Simons, Dirk and Stoltenberg, J and Sureth-Sloane, Caren}, year={2022}, pages={824–829} }"},"year":"2022","issue":"22","publication_status":"published","title":"Chancen und Risiken eines Cooperative Compliance-Ansatzes für die deutsche Besteuerungspraxis von multinationalen Unternehmen – Erfahrungen verschiedener Länder und Eindrücke deutscher Unternehmensvertreter","volume":31,"date_created":"2023-01-10T10:18:09Z","author":[{"full_name":"Arbeitskreis Verrechnungspreise der Schmalenbach-Gesellschaft für Betriebswirtschaftslehre e.V., .","last_name":"Arbeitskreis Verrechnungspreise der Schmalenbach-Gesellschaft für Betriebswirtschaftslehre e.V.","first_name":"."},{"first_name":"A","last_name":"lead authors: Kreuzer","full_name":"lead authors: Kreuzer, A"},{"first_name":"H","last_name":"Maier","full_name":"Maier, H"},{"first_name":"J. T.","full_name":"Martini, J. T.","last_name":"Martini"},{"first_name":"Rainer","full_name":"Niemann, Rainer","last_name":"Niemann"},{"first_name":"Maite","full_name":"Schachtebeck, Maite","last_name":"Schachtebeck"},{"first_name":"Dirk","last_name":"Simons","full_name":"Simons, Dirk"},{"last_name":"Stoltenberg","full_name":"Stoltenberg, J","first_name":"J"},{"first_name":"Caren","orcid":" 0000-0002-8183-5901","last_name":"Sureth-Sloane","id":"530","full_name":"Sureth-Sloane, Caren"}],"date_updated":"2024-04-11T12:05:34Z","status":"public","publication":"Internationales Steuerrecht","type":"journal_article","language":[{"iso":"ger"}],"department":[{"_id":"187"}],"user_id":"74000","_id":"35749"},{"abstract":[{"lang":"eng","text":"We define invariants $\\operatorname{inv}_1,\\dots,\\operatorname{inv}_m$ of\r\nGalois extensions of number fields with a fixed Galois group. Then, we propose\r\na heuristic in the spirit of Malle's conjecture which asymptotically predicts\r\nthe number of extensions that satisfy $\\operatorname{inv}_i\\leq X_i$ for all\r\n$X_i$. The resulting conjecture is proved for abelian Galois groups. We also\r\ndescribe refined Artin conductors that carry essentially the same information\r\nas the invariants $\\operatorname{inv}_1,\\dots,\\operatorname{inv}_m$."}],"status":"public","publication":"arXiv:2211.16698","type":"preprint","language":[{"iso":"eng"}],"extern":"1","_id":"53421","external_id":{"arxiv":["2211.16698"]},"user_id":"100450","year":"2022","citation":{"ama":"Gundlach F. Malle’s conjecture with multiple invariants. <i>arXiv:221116698</i>. Published online 2022.","ieee":"F. 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Tavana, H. Kian, A.K. Nasr, K. Govindan, H. Mina, Journal of Cleaner Production 332 (2022).","apa":"Tavana, M., Kian, H., Nasr, A. K., Govindan, K., &#38; Mina, H. (2022). A comprehensive framework for sustainable closed-loop supply chain network design. <i>Journal of Cleaner Production</i>, <i>332</i>, Article 129777. <a href=\"https://doi.org/10.1016/j.jclepro.2021.129777\">https://doi.org/10.1016/j.jclepro.2021.129777</a>","chicago":"Tavana, Madjid, Hadi Kian, Arash Khalili Nasr, Kannan Govindan, and Hassan Mina. “A Comprehensive Framework for Sustainable Closed-Loop Supply Chain Network Design.” <i>Journal of Cleaner Production</i> 332 (2022). <a href=\"https://doi.org/10.1016/j.jclepro.2021.129777\">https://doi.org/10.1016/j.jclepro.2021.129777</a>.","ieee":"M. Tavana, H. Kian, A. K. Nasr, K. Govindan, and H. 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