# American Institute of Mathematical Sciences

doi: 10.3934/eect.2020040

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

 School of Mathematical Sciences, Shanxi University, Taiyuan 030006, China

* Corresponding author: Wenbin Lv

Received  July 2019 Revised  November 2019 Published  March 2020

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
 $\lambda\in\mathbb{R}, \, \mu>0$
and
 $l>2$
are constants, then for all sufficiently smooth initial data the system
 $\left\{ \begin{array}{l}{u_t} = \Delta (\gamma (v)u) + \lambda u - \mu {u^l},\;\;\;\;\;x \in \Omega ,{\mkern 1mu} t > 0,\;\\{v_t} = \Delta v - v + u,\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;x \in \Omega ,{\mkern 1mu} t > 0,\end{array} \right.$
possesses a global classical solution.
Citation: Wenbin Lv, Qingyuan Wang. Global existence for a class of Keller-Segel models with signal-dependent motility and general logistic term. Evolution Equations & Control Theory, doi: 10.3934/eect.2020040
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