@article{63312,
  abstract     = {{<jats:p xml:lang="fr">&lt;p style='text-indent:20px;'&gt;The chemotaxis system&lt;/p&gt;&lt;p style='text-indent:20px;'&gt;&lt;disp-formula&gt; &lt;label/&gt; &lt;tex-math id="FE1"&gt; \begin{document}$ \begin{array}{l}\left\{ \begin{array}{l} 	u_t = \nabla \cdot \big( D(u) \nabla u \big) - \nabla \cdot \big( uS(x, u, v)\cdot \nabla v\big), \\ 	v_t = \Delta v -uv, \end{array} \right. \end{array} $\end{document} &lt;/tex-math&gt;&lt;/disp-formula&gt;&lt;/p&gt;&lt;p style='text-indent:20px;'&gt;is considered in a bounded domain &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;\begin{document}$ \Omega\subset \mathbb{R}^n $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;, &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}$ n\ge 2 $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;, with smooth boundary.&lt;/p&gt;&lt;p style='text-indent:20px;'&gt;It is shown that if &lt;inline-formula&gt;&lt;tex-math id="M3"&gt;\begin{document}$ D: [0, \infty) \to [0, \infty) $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; and &lt;inline-formula&gt;&lt;tex-math id="M4"&gt;\begin{document}$ S: \overline{\Omega}\times [0, \infty)\times (0, \infty)\to \mathbb{R}^{n\times n} $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; are suitably smooth functions satisfying&lt;/p&gt;&lt;p style='text-indent:20px;'&gt;&lt;disp-formula&gt; &lt;label/&gt; &lt;tex-math id="FE2"&gt; \begin{document}$ \begin{array}{l}D(u) \ge k_D u^{m-1} 	\qquad {\rm{for\; all}}\; u\ge 0 \end{array} $\end{document} &lt;/tex-math&gt;&lt;/disp-formula&gt;&lt;/p&gt;&lt;p style='text-indent:20px;'&gt;and&lt;/p&gt;&lt;p style='text-indent:20px;'&gt;&lt;disp-formula&gt; &lt;label/&gt; &lt;tex-math id="FE3"&gt; \begin{document}$ \begin{array}{l}|S(x, u, v)| \le \frac{S_0(v)}{v^\alpha} \qquad {\rm{for\; all}}\; (x, u, v)\; \in \Omega\times (0, \infty)^2 \end{array} $\end{document} &lt;/tex-math&gt;&lt;/disp-formula&gt;&lt;/p&gt;&lt;p style='text-indent:20px;'&gt;with some&lt;/p&gt;&lt;p style='text-indent:20px;'&gt;&lt;disp-formula&gt; &lt;label/&gt; &lt;tex-math id="FE4"&gt; \begin{document}$ \begin{array}{l}m&amp;gt;\frac{3n-2}{2n} 	\qquad {\rm{and}}\;\alpha\in [0, 1), \end{array} $\end{document} &lt;/tex-math&gt;&lt;/disp-formula&gt;&lt;/p&gt;&lt;p style='text-indent:20px;'&gt;and with some &lt;inline-formula&gt;&lt;tex-math id="M5"&gt;\begin{document}$ k_D&amp;gt;0 $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; and nondecreasing &lt;inline-formula&gt;&lt;tex-math id="M6"&gt;\begin{document}$ S_0: (0, \infty)\to (0, \infty) $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;, then for all suitably regular initial data a corresponding no-flux type initial-boundary value problem admits a global bounded weak solution which actually is smooth and classical if &lt;inline-formula&gt;&lt;tex-math id="M7"&gt;\begin{document}$ D(0)&amp;gt;0 $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;.&lt;/p&gt;</jats:p>}},
  author       = {{Winkler, Michael}},
  issn         = {{1531-3492}},
  journal      = {{Discrete and Continuous Dynamical Systems - B}},
  number       = {{11}},
  publisher    = {{American Institute of Mathematical Sciences (AIMS)}},
  title        = {{{Approaching logarithmic singularities in quasilinear chemotaxis-consumption systems with signal-dependent sensitivities}}},
  doi          = {{10.3934/dcdsb.2022009}},
  volume       = {{27}},
  year         = {{2022}},
}

@article{63330,
  author       = {{Li, Genglin and Tao, Youshan and Winkler, Michael}},
  issn         = {{1531-3492}},
  journal      = {{Discrete and Continuous Dynamical Systems - B}},
  number       = {{11}},
  pages        = {{4383--4396}},
  publisher    = {{American Institute of Mathematical Sciences (AIMS)}},
  title        = {{{Large time behavior in a predator-prey system with indirect pursuit-evasion interaction}}},
  doi          = {{10.3934/dcdsb.2020102}},
  volume       = {{25}},
  year         = {{2020}},
}

@article{34663,
  author       = {{Black, Tobias}},
  issn         = {{1553-524X}},
  journal      = {{Discrete &amp; Continuous Dynamical Systems - B}},
  keywords     = {{Applied Mathematics, Discrete Mathematics and Combinatorics}},
  number       = {{4}},
  pages        = {{1253--1272}},
  publisher    = {{American Institute of Mathematical Sciences (AIMS)}},
  title        = {{{Global existence and asymptotic stability in a competitive two-species chemotaxis system with two signals}}},
  doi          = {{10.3934/dcdsb.2017061}},
  volume       = {{22}},
  year         = {{2017}},
}