Global existence for a class of Keller-Segel models with signal-dependent motility and general logistic term

Abstract

<p style='text-indent:20px;'>This paper focuses on the global existence for a class of Keller-Segel models with signal-dependent motility and general logistic term under homogeneous Neumann boundary conditions in a two-dimensional smoothly bounded domain. We show that if <inline-formula><tex-math id="M1">\begin{document}$ \lambda\in\mathbb{R}, \, \mu&gt;0 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M2">\begin{document}$ l&gt;2 $\end{document}</tex-math></inline-formula> are constants, then for all sufficiently smooth initial data the system <p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$\left\{ \begin{array}{l}{u_t} = \Delta (\gamma (v)u) + \lambda u - \mu {u^l},\;\;\;\;\;x \in \Omega ,{\mkern 1mu} t &gt; 0,\;\\{v_t} = \Delta v - v + u,\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;x \in \Omega ,{\mkern 1mu} t &gt; 0,\end{array} \right.$\end{document} </tex-math></disp-formula> <p style='text-indent:20px;'>possesses a global classical solution.