@inproceedings{52339,
  author       = {{Intveen, Julie}},
  booktitle    = {{Media Literacy in Language (Teacher) Education }},
  location     = {{Universität Erfurt}},
  title        = {{{Fictions of Identity – A Didactic Approach to Serial Literacy}}},
  year         = {{2023}},
}

@article{53142,
  author       = {{Berger, Thomas and Lanza, Lukas}},
  journal      = {{IMA Journal of Mathematical Control and Information,}},
  number       = {{4}},
  pages        = {{691--713}},
  title        = {{{Funnel control of linear systems with arbitrary relative degree under output measurement losses}}},
  doi          = {{doi: 10.1093/imamci/dnad029}},
  volume       = {{40}},
  year         = {{2023}},
}

@article{53143,
  author       = {{Lee, J. G. and Berger, Thomas and Trenn, S. and Shim, H.}},
  journal      = {{Automatica}},
  pages        = {{Article 111204}},
  title        = {{{Edge-wise funnel output synchronization of heterogeneous agents with relative degree one}}},
  doi          = {{doi: 10.1016/j.automatica.2023.111204 (open access)}},
  volume       = {{156}},
  year         = {{2023}},
}

@inproceedings{53260,
  author       = {{Soleymani, Mohammad and Santamaria, Ignacio and Jorswieck, Eduard}},
  booktitle    = {{2023 31st European Signal Processing Conference (EUSIPCO)}},
  publisher    = {{IEEE}},
  title        = {{{Energy-Efficient Rate Splitting for MIMO STAR-RIS-Assisted Broadcast Channels with I/Q Imbalance}}},
  doi          = {{10.23919/eusipco58844.2023.10289964}},
  year         = {{2023}},
}

@article{53262,
  author       = {{Santamaria, Ignacio and Soleymani, Mohammad and Jorswieck, Eduard and Gutiérrez, Jesús}},
  issn         = {{1070-9908}},
  journal      = {{IEEE Signal Processing Letters}},
  keywords     = {{Applied Mathematics, Electrical and Electronic Engineering, Signal Processing}},
  pages        = {{923--926}},
  publisher    = {{Institute of Electrical and Electronics Engineers (IEEE)}},
  title        = {{{SNR Maximization in Beyond Diagonal RIS-Assisted Single and Multiple Antenna Links}}},
  doi          = {{10.1109/lsp.2023.3296902}},
  volume       = {{30}},
  year         = {{2023}},
}

@article{53261,
  author       = {{Soleymani, Mohammad and Santamaria, Ignacio and Jorswieck, Eduard and Clerckx, Bruno}},
  issn         = {{1536-1276}},
  journal      = {{IEEE Transactions on Wireless Communications}},
  keywords     = {{Applied Mathematics, Electrical and Electronic Engineering, Computer Science Applications}},
  pages        = {{1--1}},
  publisher    = {{Institute of Electrical and Electronics Engineers (IEEE)}},
  title        = {{{Optimization of Rate-Splitting Multiple Access in Beyond Diagonal RIS-assisted URLLC Systems}}},
  doi          = {{10.1109/twc.2023.3324190}},
  year         = {{2023}},
}

@article{53265,
  author       = {{Soleymani, Mohammad and Santamaria, Ignacio and Jorswieck, Eduard and Rezvani, Sepehr}},
  issn         = {{1053-587X}},
  journal      = {{IEEE Transactions on Signal Processing}},
  keywords     = {{Electrical and Electronic Engineering, Signal Processing}},
  pages        = {{963--978}},
  publisher    = {{Institute of Electrical and Electronics Engineers (IEEE)}},
  title        = {{{NOMA-Based Improper Signaling for Multicell MISO RIS-Assisted Broadcast Channels}}},
  doi          = {{10.1109/tsp.2023.3259145}},
  volume       = {{71}},
  year         = {{2023}},
}

@article{53263,
  author       = {{Soleymani, Mohammad and Santamaria, Ignacio and Jorswieck, Eduard A.}},
  issn         = {{2169-3536}},
  journal      = {{IEEE Access}},
  keywords     = {{General Engineering, General Materials Science, General Computer Science, Electrical and Electronic Engineering}},
  pages        = {{70833--70852}},
  publisher    = {{Institute of Electrical and Electronics Engineers (IEEE)}},
  title        = {{{Spectral and Energy Efficiency Maximization of MISO STAR-RIS-Assisted URLLC Systems}}},
  doi          = {{10.1109/access.2023.3294092}},
  volume       = {{11}},
  year         = {{2023}},
}

@inproceedings{53264,
  author       = {{Santamaria, Ignacio and Soleymani, Mohammad and Jorswieck, Eduard and Gutiérrez, Jesús}},
  booktitle    = {{ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}},
  publisher    = {{IEEE}},
  title        = {{{Interference Leakage Minimization in RIS-Assisted MIMO Interference Channels}}},
  doi          = {{10.1109/icassp49357.2023.10094656}},
  year         = {{2023}},
}

@article{53301,
  author       = {{Vieluf, Solveig and Hasija, Tanuj and Kuschel, Maurice and Reinsberger, Claus and Loddenkemper, Tobias}},
  issn         = {{0957-4174}},
  journal      = {{Expert Systems with Applications}},
  keywords     = {{Artificial Intelligence, Computer Science Applications, General Engineering}},
  publisher    = {{Elsevier BV}},
  title        = {{{Developing a deep canonical correlation-based technique for seizure prediction}}},
  doi          = {{10.1016/j.eswa.2023.120986}},
  volume       = {{234}},
  year         = {{2023}},
}

@inproceedings{53303,
  author       = {{Kuschel, Maurice and Marrinan, Timothy and Hasija, Tanuj}},
  booktitle    = {{2023 IEEE 33rd International Workshop on Machine Learning for Signal Processing (MLSP)}},
  publisher    = {{IEEE}},
  title        = {{{Geodesic-Based Relaxation For Deep Canonical Correlation Analysis}}},
  doi          = {{10.1109/mlsp55844.2023.10285937}},
  year         = {{2023}},
}

@inproceedings{53310,
  author       = {{Gedlu, Emebet Gebeyehu and Wallscheid, Oliver and Böcker, Joachim and Nelles, Oliver}},
  booktitle    = {{2023 IEEE 14th International Symposium on Diagnostics for Electrical Machines, Power Electronics and Drives (SDEMPED)}},
  publisher    = {{IEEE}},
  title        = {{{Online system identification and excitation for thermal monitoring of electric machines using machine learning and model predictive control}}},
  doi          = {{10.1109/sdemped54949.2023.10271427}},
  year         = {{2023}},
}

@article{53317,
  author       = {{Tao, Youshan and Winkler, Michael}},
  issn         = {{2163-2480}},
  journal      = {{Evolution Equations and Control Theory}},
  keywords     = {{Applied Mathematics, Control and Optimization, Modeling and Simulation}},
  number       = {{6}},
  pages        = {{1676--1687}},
  publisher    = {{American Institute of Mathematical Sciences (AIMS)}},
  title        = {{{Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities}}},
  doi          = {{10.3934/eect.2023031}},
  volume       = {{12}},
  year         = {{2023}},
}

@article{53320,
  author       = {{Winkler, Michael}},
  issn         = {{0294-1449}},
  journal      = {{Annales de l'Institut Henri Poincaré C, Analyse non linéaire}},
  keywords     = {{Mathematical Physics, Analysis, Applied Mathematics}},
  publisher    = {{European Mathematical Society - EMS - Publishing House GmbH}},
  title        = {{{A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion}}},
  doi          = {{10.4171/aihpc/73}},
  year         = {{2023}},
}

@article{53318,
  author       = {{Li, Genglin and Winkler, Michael}},
  issn         = {{0003-6811}},
  journal      = {{Applicable Analysis}},
  keywords     = {{Applied Mathematics, Analysis}},
  number       = {{1}},
  pages        = {{45--64}},
  publisher    = {{Informa UK Limited}},
  title        = {{{Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities}}},
  doi          = {{10.1080/00036811.2023.2173183}},
  volume       = {{103}},
  year         = {{2023}},
}

@article{53328,
  abstract     = {{<jats:p> As a simplified version of a three-component taxis cascade model accounting for different migration strategies of two population groups in search of food, a two-component nonlocal nutrient taxis system is considered in a two-dimensional bounded convex domain with smooth boundary. For any given conveniently regular and biologically meaningful initial data, smallness conditions on the prescribed resource growth and on the initial nutrient signal concentration are identified which ensure the global existence of a global classical solution to the corresponding no-flux initial-boundary value problem. Moreover, under additional assumptions on the food production source these solutions are shown to be bounded, and to stabilize toward semi-trivial equilibria in the large time limit, respectively. </jats:p>}},
  author       = {{Tao, Youshan and Winkler, Michael}},
  issn         = {{0218-2025}},
  journal      = {{Mathematical Models and Methods in Applied Sciences}},
  keywords     = {{Applied Mathematics, Modeling and Simulation}},
  number       = {{01}},
  pages        = {{103--138}},
  publisher    = {{World Scientific Pub Co Pte Ltd}},
  title        = {{{Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers}}},
  doi          = {{10.1142/s0218202523500045}},
  volume       = {{33}},
  year         = {{2023}},
}

@article{53324,
  author       = {{Ahn, Jaewook and Winkler, Michael}},
  issn         = {{0944-2669}},
  journal      = {{Calculus of Variations and Partial Differential Equations}},
  keywords     = {{Applied Mathematics, Analysis}},
  number       = {{6}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system}}},
  doi          = {{10.1007/s00526-023-02523-5}},
  volume       = {{62}},
  year         = {{2023}},
}

@article{53329,
  author       = {{Tao, Youshan and Winkler, Michael}},
  issn         = {{1468-1218}},
  journal      = {{Nonlinear Analysis: Real World Applications}},
  keywords     = {{Applied Mathematics, Computational Mathematics, General Economics, Econometrics and Finance, General Engineering, General Medicine, Analysis}},
  publisher    = {{Elsevier BV}},
  title        = {{{Analysis of a chemotaxis-SIS epidemic model with unbounded infection force}}},
  doi          = {{10.1016/j.nonrwa.2022.103820}},
  volume       = {{71}},
  year         = {{2023}},
}

@article{53326,
  author       = {{Li, Genglin and Winkler, Michael}},
  issn         = {{1539-6746}},
  journal      = {{Communications in Mathematical Sciences}},
  keywords     = {{Applied Mathematics, General Mathematics}},
  number       = {{2}},
  pages        = {{299--322}},
  publisher    = {{International Press of Boston}},
  title        = {{{Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities}}},
  doi          = {{10.4310/cms.2023.v21.n2.a1}},
  volume       = {{21}},
  year         = {{2023}},
}

@article{53343,
  abstract     = {{<jats:title>Abstract</jats:title>
               <jats:p>The Cauchy problem in <jats:inline-formula>
                     <jats:alternatives>
                        <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_math-2022-0578_eq_001.png" />
                        <m:math xmlns:m="http://www.w3.org/1998/Math/MathML">
                           <m:msup>
                              <m:mrow>
                                 <m:mi mathvariant="double-struck">R</m:mi>
                              </m:mrow>
                              <m:mrow>
                                 <m:mi>n</m:mi>
                              </m:mrow>
                           </m:msup>
                        </m:math>
                        <jats:tex-math>{{\mathbb{R}}}^{n}</jats:tex-math>
                     </jats:alternatives>
                  </jats:inline-formula>, <jats:inline-formula>
                     <jats:alternatives>
                        <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_math-2022-0578_eq_002.png" />
                        <m:math xmlns:m="http://www.w3.org/1998/Math/MathML">
                           <m:mi>n</m:mi>
                           <m:mo>≥</m:mo>
                           <m:mn>2</m:mn>
                        </m:math>
                        <jats:tex-math>n\ge 2</jats:tex-math>
                     </jats:alternatives>
                  </jats:inline-formula>, for <jats:disp-formula id="j_math-2022-0578_eq_001">
                     <jats:alternatives>
                        <jats:graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_math-2022-0578_eq_003.png" />
                        <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="block">
                           <m:mtable displaystyle="true">
                              <m:mtr>
                                 <m:mtd columnalign="right">
                                    <m:mfenced open="{" close="">
                                       <m:mrow>
                                          <m:mspace depth="1.25em" />
                                          <m:mtable displaystyle="true">
                                             <m:mtr>
                                                <m:mtd columnalign="left">
                                                   <m:msub>
                                                      <m:mrow>
                                                         <m:mi>u</m:mi>
                                                      </m:mrow>
                                                      <m:mrow>
                                                         <m:mi>t</m:mi>
                                                      </m:mrow>
                                                   </m:msub>
                                                   <m:mo>=</m:mo>
                                                   <m:mi mathvariant="normal">Δ</m:mi>
                                                   <m:mi>u</m:mi>
                                                   <m:mo>−</m:mo>
                                                   <m:mrow>
                                                      <m:mo>∇</m:mo>
                                                   </m:mrow>
                                                   <m:mo>⋅</m:mo>
                                                   <m:mrow>
                                                      <m:mo>(</m:mo>
                                                      <m:mrow>
                                                         <m:mi>u</m:mi>
                                                         <m:mi>S</m:mi>
                                                         <m:mo>⋅</m:mo>
                                                         <m:mrow>
                                                            <m:mo>∇</m:mo>
                                                         </m:mrow>
                                                         <m:mi>v</m:mi>
                                                      </m:mrow>
                                                      <m:mo>)</m:mo>
                                                   </m:mrow>
                                                   <m:mo>,</m:mo>
                                                </m:mtd>
                                             </m:mtr>
                                             <m:mtr>
                                                <m:mtd columnalign="left">
                                                   <m:mn>0</m:mn>
                                                   <m:mo>=</m:mo>
                                                   <m:mi mathvariant="normal">Δ</m:mi>
                                                   <m:mi>v</m:mi>
                                                   <m:mo>+</m:mo>
                                                   <m:mi>u</m:mi>
                                                   <m:mo>,</m:mo>
                                                </m:mtd>
                                             </m:mtr>
                                          </m:mtable>
                                       </m:mrow>
                                    </m:mfenced>
                                    <m:mspace width="2.0em" />
                                    <m:mspace width="2.0em" />
                                    <m:mspace width="2.0em" />
                                    <m:mrow>
                                       <m:mo>(</m:mo>
                                       <m:mrow>
                                          <m:mo>⋆</m:mo>
                                       </m:mrow>
                                       <m:mo>)</m:mo>
                                    </m:mrow>
                                 </m:mtd>
                              </m:mtr>
                           </m:mtable>
                        </m:math>
                        <jats:tex-math>\begin{array}{r}\left\{\phantom{\rule[-1.25em]{}{0ex}}\begin{array}{l}{u}_{t}=\Delta u-\nabla \cdot \left(uS\cdot \nabla v),\\ 0=\Delta v+u,\end{array}\right.\hspace{2.0em}\hspace{2.0em}\hspace{2.0em}\left(\star )\end{array}</jats:tex-math>
                     </jats:alternatives>
                  </jats:disp-formula> is considered for general matrices <jats:inline-formula>
                     <jats:alternatives>
                        <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_math-2022-0578_eq_004.png" />
                        <m:math xmlns:m="http://www.w3.org/1998/Math/MathML">
                           <m:mi>S</m:mi>
                           <m:mo>∈</m:mo>
                           <m:msup>
                              <m:mrow>
                                 <m:mi mathvariant="double-struck">R</m:mi>
                              </m:mrow>
                              <m:mrow>
                                 <m:mi>n</m:mi>
                                 <m:mo>×</m:mo>
                                 <m:mi>n</m:mi>
                              </m:mrow>
                           </m:msup>
                        </m:math>
                        <jats:tex-math>S\in {{\mathbb{R}}}^{n\times n}</jats:tex-math>
                     </jats:alternatives>
                  </jats:inline-formula>. A theory of local-in-time classical existence and extensibility is developed in a framework that differs from those considered in large parts of the literature by involving bounded classical solutions. Specifically, it is shown that for all non-negative initial data belonging to <jats:inline-formula>
                     <jats:alternatives>
                        <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_math-2022-0578_eq_005.png" />
                        <m:math xmlns:m="http://www.w3.org/1998/Math/MathML">
                           <m:mi mathvariant="normal">BUC</m:mi>
                           <m:mrow>
                              <m:mo>(</m:mo>
                              <m:mrow>
                                 <m:msup>
                                    <m:mrow>
                                       <m:mi mathvariant="double-struck">R</m:mi>
                                    </m:mrow>
                                    <m:mrow>
                                       <m:mi>n</m:mi>
                                    </m:mrow>
                                 </m:msup>
                              </m:mrow>
                              <m:mo>)</m:mo>
                           </m:mrow>
                           <m:mo>∩</m:mo>
                           <m:msup>
                              <m:mrow>
                                 <m:mi>L</m:mi>
                              </m:mrow>
                              <m:mrow>
                                 <m:mi>p</m:mi>
                              </m:mrow>
                           </m:msup>
                           <m:mrow>
                              <m:mo>(</m:mo>
                              <m:mrow>
                                 <m:msup>
                                    <m:mrow>
                                       <m:mi mathvariant="double-struck">R</m:mi>
                                    </m:mrow>
                                    <m:mrow>
                                       <m:mi>n</m:mi>
                                    </m:mrow>
                                 </m:msup>
                              </m:mrow>
                              <m:mo>)</m:mo>
                           </m:mrow>
                        </m:math>
                        <jats:tex-math>{\rm{BUC}}\left({{\mathbb{R}}}^{n})\cap {L}^{p}\left({{\mathbb{R}}}^{n})</jats:tex-math>
                     </jats:alternatives>
                  </jats:inline-formula> with some <jats:inline-formula>
                     <jats:alternatives>
                        <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_math-2022-0578_eq_006.png" />
                        <m:math xmlns:m="http://www.w3.org/1998/Math/MathML">
                           <m:mi>p</m:mi>
                           <m:mo>∈</m:mo>
                           <m:mrow>
                              <m:mo>[</m:mo>
                              <m:mrow>
                                 <m:mn>1</m:mn>
                                 <m:mo>,</m:mo>
                                 <m:mi>n</m:mi>
                              </m:mrow>
                              <m:mo>)</m:mo>
                           </m:mrow>
                        </m:math>
                        <jats:tex-math>p\in \left[1,n)</jats:tex-math>
                     </jats:alternatives>
                  </jats:inline-formula>, there exist <jats:inline-formula>
                     <jats:alternatives>
                        <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_math-2022-0578_eq_007.png" />
                        <m:math xmlns:m="http://www.w3.org/1998/Math/MathML">
                           <m:msub>
                              <m:mrow>
                                 <m:mi>T</m:mi>
                              </m:mrow>
                              <m:mrow>
                                 <m:mi>max</m:mi>
                              </m:mrow>
                           </m:msub>
                           <m:mo>∈</m:mo>
                           <m:mrow>
                              <m:mo>(</m:mo>
                              <m:mrow>
                                 <m:mn>0</m:mn>
                                 <m:mo>,</m:mo>
                                 <m:mi>∞</m:mi>
                              </m:mrow>
                              <m:mo>]</m:mo>
                           </m:mrow>
                        </m:math>
                        <jats:tex-math>{T}_{\max }\in \left(0,\infty ]</jats:tex-math>
                     </jats:alternatives>
                  </jats:inline-formula> and a uniquely determined <jats:inline-formula>
                     <jats:alternatives>
                        <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_math-2022-0578_eq_008.png" />
                        <m:math xmlns:m="http://www.w3.org/1998/Math/MathML">
                           <m:mi>u</m:mi>
                           <m:mo>∈</m:mo>
                           <m:msup>
                              <m:mrow>
                                 <m:mi>C</m:mi>
                              </m:mrow>
                              <m:mrow>
                                 <m:mn>0</m:mn>
                              </m:mrow>
                           </m:msup>
                           <m:mrow>
                              <m:mo>(</m:mo>
                              <m:mrow>
                                 <m:mrow>
                                    <m:mo>[</m:mo>
                                    <m:mrow>
                                       <m:mn>0</m:mn>
                                       <m:mo>,</m:mo>
                                       <m:msub>
                                          <m:mrow>
                                             <m:mi>T</m:mi>
                                          </m:mrow>
                                          <m:mrow>
                                             <m:mi>max</m:mi>
                                          </m:mrow>
                                       </m:msub>
                                    </m:mrow>
                                    <m:mo>)</m:mo>
                                 </m:mrow>
                                 <m:mo>;</m:mo>
                                 <m:mspace width="0.33em" />
                                 <m:mi mathvariant="normal">BUC</m:mi>
                                 <m:mrow>
                                    <m:mo>(</m:mo>
                                    <m:mrow>
                                       <m:msup>
                                          <m:mrow>
                                             <m:mi mathvariant="double-struck">R</m:mi>
                                          </m:mrow>
                                          <m:mrow>
                                             <m:mi>n</m:mi>
                                          </m:mrow>
                                       </m:msup>
                                    </m:mrow>
                                    <m:mo>)</m:mo>
                                 </m:mrow>
                              </m:mrow>
                              <m:mo>)</m:mo>
                           </m:mrow>
                           <m:mo>∩</m:mo>
                           <m:msup>
                              <m:mrow>
                                 <m:mi>C</m:mi>
                              </m:mrow>
                              <m:mrow>
                                 <m:mn>0</m:mn>
                              </m:mrow>
                           </m:msup>
                           <m:mrow>
                              <m:mo>(</m:mo>
                              <m:mrow>
                                 <m:mrow>
                                    <m:mo>[</m:mo>
                                    <m:mrow>
                                       <m:mn>0</m:mn>
                                       <m:mo>,</m:mo>
                                       <m:msub>
                                          <m:mrow>
                                             <m:mi>T</m:mi>
                                          </m:mrow>
                                          <m:mrow>
                                             <m:mi>max</m:mi>
                                          </m:mrow>
                                       </m:msub>
                                    </m:mrow>
                                    <m:mo>)</m:mo>
                                 </m:mrow>
                                 <m:mo>;</m:mo>
                                 <m:mspace width="0.33em" />
                                 <m:msup>
                                    <m:mrow>
                                       <m:mi>L</m:mi>
                                    </m:mrow>
                                    <m:mrow>
                                       <m:mi>p</m:mi>
                                    </m:mrow>
                                 </m:msup>
                                 <m:mrow>
                                    <m:mo>(</m:mo>
                                    <m:mrow>
                                       <m:msup>
                                          <m:mrow>
                                             <m:mi mathvariant="double-struck">R</m:mi>
                                          </m:mrow>
                                          <m:mrow>
                                             <m:mi>n</m:mi>
                                          </m:mrow>
                                       </m:msup>
                                    </m:mrow>
                                    <m:mo>)</m:mo>
                                 </m:mrow>
                              </m:mrow>
                              <m:mo>)</m:mo>
                           </m:mrow>
                           <m:mo>∩</m:mo>
                           <m:msup>
                              <m:mrow>
                                 <m:mi>C</m:mi>
                              </m:mrow>
                              <m:mrow>
                                 <m:mi>∞</m:mi>
                              </m:mrow>
                           </m:msup>
                           <m:mrow>
                              <m:mo>(</m:mo>
                              <m:mrow>
                                 <m:msup>
                                    <m:mrow>
                                       <m:mi mathvariant="double-struck">R</m:mi>
                                    </m:mrow>
                                    <m:mrow>
                                       <m:mi>n</m:mi>
                                    </m:mrow>
                                 </m:msup>
                                 <m:mo>×</m:mo>
                                 <m:mrow>
                                    <m:mo>(</m:mo>
                                    <m:mrow>
                                       <m:mn>0</m:mn>
                                       <m:mo>,</m:mo>
                                       <m:msub>
                                          <m:mrow>
                                             <m:mi>T</m:mi>
                                          </m:mrow>
                                          <m:mrow>
                                             <m:mi>max</m:mi>
                                          </m:mrow>
                                       </m:msub>
                                    </m:mrow>
                                    <m:mo>)</m:mo>
                                 </m:mrow>
                              </m:mrow>
                              <m:mo>)</m:mo>
                           </m:mrow>
                        </m:math>
                        <jats:tex-math>u\in {C}^{0}\left(\left[0,{T}_{\max });\hspace{0.33em}{\rm{BUC}}\left({{\mathbb{R}}}^{n}))\cap {C}^{0}\left(\left[0,{T}_{\max });\hspace{0.33em}{L}^{p}\left({{\mathbb{R}}}^{n}))\cap {C}^{\infty }\left({{\mathbb{R}}}^{n}\times \left(0,{T}_{\max }))</jats:tex-math>
                     </jats:alternatives>
                  </jats:inline-formula> such that with <jats:inline-formula>
                     <jats:alternatives>
                        <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_math-2022-0578_eq_009.png" />
                        <m:math xmlns:m="http://www.w3.org/1998/Math/MathML">
                           <m:mi>v</m:mi>
                           <m:mo>≔</m:mo>
                           <m:mi mathvariant="normal">Γ</m:mi>
                           <m:mo>⋆</m:mo>
                           <m:mi>u</m:mi>
                        </m:math>
                        <jats:tex-math>v:= \Gamma \star u</jats:tex-math>
                     </jats:alternatives>
                  </jats:inline-formula>, and with <jats:inline-formula>
                     <jats:alternatives>
                        <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_math-2022-0578_eq_010.png" />
                        <m:math xmlns:m="http://www.w3.org/1998/Math/MathML">
                           <m:mi mathvariant="normal">Γ</m:mi>
                        </m:math>
                        <jats:tex-math>\Gamma </jats:tex-math>
                     </jats:alternatives>
                  </jats:inline-formula> denoting the Newtonian kernel on <jats:inline-formula>
                     <jats:alternatives>
                        <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_math-2022-0578_eq_011.png" />
                        <m:math xmlns:m="http://www.w3.org/1998/Math/MathML">
                           <m:msup>
                              <m:mrow>
                                 <m:mi mathvariant="double-struck">R</m:mi>
                              </m:mrow>
                              <m:mrow>
                                 <m:mi>n</m:mi>
                              </m:mrow>
                           </m:msup>
                        </m:math>
                        <jats:tex-math>{{\mathbb{R}}}^{n}</jats:tex-math>
                     </jats:alternatives>
                  </jats:inline-formula>, the pair <jats:inline-formula>
                     <jats:alternatives>
                        <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_math-2022-0578_eq_012.png" />
                        <m:math xmlns:m="http://www.w3.org/1998/Math/MathML">
                           <m:mrow>
                              <m:mo>(</m:mo>
                              <m:mrow>
                                 <m:mi>u</m:mi>
                                 <m:mo>,</m:mo>
                                 <m:mi>v</m:mi>
                              </m:mrow>
                              <m:mo>)</m:mo>
                           </m:mrow>
                        </m:math>
                        <jats:tex-math>\left(u,v)</jats:tex-math>
                     </jats:alternatives>
                  </jats:inline-formula> forms a classical solution of (<jats:inline-formula>
                     <jats:alternatives>
                        <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_math-2022-0578_eq_013.png" />
                        <m:math xmlns:m="http://www.w3.org/1998/Math/MathML">
                           <m:mo>⋆</m:mo>
                        </m:math>
                        <jats:tex-math>\star </jats:tex-math>
                     </jats:alternatives>
                  </jats:inline-formula>) in <jats:inline-formula>
                     <jats:alternatives>
                        <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_math-2022-0578_eq_014.png" />
                        <m:math xmlns:m="http://www.w3.org/1998/Math/MathML">
                           <m:msup>
                              <m:mrow>
                                 <m:mi mathvariant="double-struck">R</m:mi>
                              </m:mrow>
                              <m:mrow>
                                 <m:mi>n</m:mi>
                              </m:mrow>
                           </m:msup>
                           <m:mo>×</m:mo>
                           <m:mrow>
                              <m:mo>(</m:mo>
                              <m:mrow>
                                 <m:mn>0</m:mn>
                                 <m:mo>,</m:mo>
                                 <m:msub>
                                    <m:mrow>
                                       <m:mi>T</m:mi>
                                    </m:mrow>
                                    <m:mrow>
                                       <m:mi>max</m:mi>
                                    </m:mrow>
                                 </m:msub>
                              </m:mrow>
                              <m:mo>)</m:mo>
                           </m:mrow>
                        </m:math>
                        <jats:tex-math>{{\mathbb{R}}}^{n}\times \left(0,{T}_{\max })</jats:tex-math>
                     </jats:alternatives>
                  </jats:inline-formula>, which has the property that <jats:disp-formula id="j_math-2022-0578_eq_002">
                     <jats:alternatives>
                        <jats:graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_math-2022-0578_eq_015.png" />
                        <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="block">
                           <m:mspace width="0.1em" />
                           <m:mtext>if</m:mtext>
                           <m:mspace width="0.1em" />
                           <m:mspace width="0.33em" />
                           <m:msub>
                              <m:mrow>
                                 <m:mi>T</m:mi>
                              </m:mrow>
                              <m:mrow>
                                 <m:mi>max</m:mi>
                              </m:mrow>
                           </m:msub>
                           <m:mo>&lt;</m:mo>
                           <m:mi>∞</m:mi>
                           <m:mo>,</m:mo>
                           <m:mspace width="1.0em" />
                           <m:mstyle>
                              <m:mspace width="0.1em" />
                              <m:mtext>then both</m:mtext>
                              <m:mspace width="0.1em" />
                           </m:mstyle>
                           <m:mspace width="0.33em" />
                           <m:munder>
                              <m:mrow>
                                 <m:mi>limsup</m:mi>
                              </m:mrow>
                              <m:mrow>
                                 <m:mi>t</m:mi>
                                 <m:mo>↗</m:mo>
                                 <m:msub>
                                    <m:mrow>
                                       <m:mi>T</m:mi>
                                    </m:mrow>
                                    <m:mrow>
                                       <m:mi>max</m:mi>
                                    </m:mrow>
                                 </m:msub>
                              </m:mrow>
                           </m:munder>
                           <m:msub>
                              <m:mrow>
                                 <m:mo>‖</m:mo>
                                 <m:mi>u</m:mi>
                                 <m:mrow>
                                    <m:mo>(</m:mo>
                                    <m:mrow>
                                       <m:mo>⋅</m:mo>
                                       <m:mo>,</m:mo>
                                       <m:mi>t</m:mi>
                                    </m:mrow>
                                    <m:mo>)</m:mo>
                                 </m:mrow>
                                 <m:mo>‖</m:mo>
                              </m:mrow>
                              <m:mrow>
                                 <m:msup>
                                    <m:mrow>
                                       <m:mi>L</m:mi>
                                    </m:mrow>
                                    <m:mrow>
                                       <m:mi>∞</m:mi>
                                    </m:mrow>
                                 </m:msup>
                                 <m:mrow>
                                    <m:mo>(</m:mo>
                                    <m:mrow>
                                       <m:msup>
                                          <m:mrow>
                                             <m:mi mathvariant="double-struck">R</m:mi>
                                          </m:mrow>
                                          <m:mrow>
                                             <m:mi>n</m:mi>
                                          </m:mrow>
                                       </m:msup>
                                    </m:mrow>
                                    <m:mo>)</m:mo>
                                 </m:mrow>
                              </m:mrow>
                           </m:msub>
                           <m:mo>=</m:mo>
                           <m:mi>∞</m:mi>
                           <m:mspace width="1.0em" />
                           <m:mspace width="0.1em" />
                           <m:mtext>and</m:mtext>
                           <m:mspace width="0.1em" />
                           <m:mspace width="1.0em" />
                           <m:munder>
                              <m:mrow>
                                 <m:mi>limsup</m:mi>
                              </m:mrow>
                              <m:mrow>
                                 <m:mi>t</m:mi>
                                 <m:mo>↗</m:mo>
                                 <m:msub>
                                    <m:mrow>
                                       <m:mi>T</m:mi>
                                    </m:mrow>
                                    <m:mrow>
                                       <m:mi>max</m:mi>
                                    </m:mrow>
                                 </m:msub>
                              </m:mrow>
                           </m:munder>
                           <m:msub>
                              <m:mrow>
                                 <m:mo>‖</m:mo>
                                 <m:mrow>
                                    <m:mo>∇</m:mo>
                                 </m:mrow>
                                 <m:mi>v</m:mi>
                                 <m:mrow>
                                    <m:mo>(</m:mo>
                                    <m:mrow>
                                       <m:mo>⋅</m:mo>
                                       <m:mo>,</m:mo>
                                       <m:mi>t</m:mi>
                                    </m:mrow>
                                    <m:mo>)</m:mo>
                                 </m:mrow>
                                 <m:mo>‖</m:mo>
                              </m:mrow>
                              <m:mrow>
                                 <m:msup>
                                    <m:mrow>
                                       <m:mi>L</m:mi>
                                    </m:mrow>
                                    <m:mrow>
                                       <m:mi>∞</m:mi>
                                    </m:mrow>
                                 </m:msup>
                                 <m:mrow>
                                    <m:mo>(</m:mo>
                                    <m:mrow>
                                       <m:msup>
                                          <m:mrow>
                                             <m:mi mathvariant="double-struck">R</m:mi>
                                          </m:mrow>
                                          <m:mrow>
                                             <m:mi>n</m:mi>
                                          </m:mrow>
                                       </m:msup>
                                    </m:mrow>
                                    <m:mo>)</m:mo>
                                 </m:mrow>
                              </m:mrow>
                           </m:msub>
                           <m:mo>=</m:mo>
                           <m:mi>∞</m:mi>
                           <m:mo>.</m:mo>
                        </m:math>
                        <jats:tex-math>\hspace{0.1em}\text{if}\hspace{0.1em}\hspace{0.33em}{T}_{\max }\lt \infty ,\hspace{1.0em}\hspace{0.1em}\text{then both}\hspace{0.1em}\hspace{0.33em}\mathop{\mathrm{limsup}}\limits_{t\nearrow {T}_{\max }}\Vert u\left(\cdot ,t){\Vert }_{{L}^{\infty }\left({{\mathbb{R}}}^{n})}=\infty \hspace{1.0em}\hspace{0.1em}\text{and}\hspace{0.1em}\hspace{1.0em}\mathop{\mathrm{limsup}}\limits_{t\nearrow {T}_{\max }}\Vert \nabla v\left(\cdot ,t){\Vert }_{{L}^{\infty }\left({{\mathbb{R}}}^{n})}=\infty .</jats:tex-math>
                     </jats:alternatives>
                  </jats:disp-formula> An exemplary application of this provides a result on global classical solvability in cases when <jats:inline-formula>
                     <jats:alternatives>
                        <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_math-2022-0578_eq_016.png" />
                        <m:math xmlns:m="http://www.w3.org/1998/Math/MathML">
                           <m:mo>∣</m:mo>
                           <m:mi>S</m:mi>
                           <m:mo>+</m:mo>
                           <m:mn mathvariant="bold">1</m:mn>
                           <m:mo>∣</m:mo>
                        </m:math>
                        <jats:tex-math>| S+{\bf{1}}| </jats:tex-math>
                     </jats:alternatives>
                  </jats:inline-formula> is sufficiently small, where <jats:inline-formula>
                     <jats:alternatives>
                        <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_math-2022-0578_eq_017.png" />
                        <m:math xmlns:m="http://www.w3.org/1998/Math/MathML">
                           <m:mn mathvariant="bold">1</m:mn>
                           <m:mo>=</m:mo>
                           <m:mi mathvariant="normal">diag</m:mi>
                           <m:mspace width="0.33em" />
                           <m:mrow>
                              <m:mo>(</m:mo>
                              <m:mrow>
                                 <m:mn>1</m:mn>
                                 <m:mo>,</m:mo>
                                 <m:mrow>
                                    <m:mo>…</m:mo>
                                 </m:mrow>
                                 <m:mo>,</m:mo>
                                 <m:mn>1</m:mn>
                              </m:mrow>
                              <m:mo>)</m:mo>
                           </m:mrow>
                        </m:math>
                        <jats:tex-math>{\bf{1}}={\rm{diag}}\hspace{0.33em}\left(1,\ldots ,1)</jats:tex-math>
                     </jats:alternatives>
                  </jats:inline-formula>.</jats:p>}},
  author       = {{Winkler, Michael}},
  issn         = {{2391-5455}},
  journal      = {{Open Mathematics}},
  keywords     = {{General Mathematics}},
  number       = {{1}},
  publisher    = {{Walter de Gruyter GmbH}},
  title        = {{{Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type}}},
  doi          = {{10.1515/math-2022-0578}},
  volume       = {{21}},
  year         = {{2023}},
}

