Electron. J. Differential Equations, Vol. 2020 (2020), No. 122, pp. 1-14.

Existence and boundedness of solutions for a Keller-Segel system with gradient dependent chemotactic sensitivity

Jianlu Yan, Yuxiang Li

Abstract:
We consider the Keller-Segel system with gradient dependent chemotactic sensitivity

in a smooth bounded domain $\Omega\subset \mathbb{R}^n$, $n\geq2$. We shown that for all reasonably regular initial data $u_0\geq 0$ and $v_0\geq0$, the corresponding Neumann initial-boundary value problem possesses a global weak solution which is uniformly bounded provided that $1<p<n/(n-1)$.

Submitted June 4, 2019. Published December 16. 2020.
Math Subject Classifications: 35K55, 35B40, 35Q92, 92C17.
Key Words: Keller-Segel system; weak solution; chemotactic sensitivity.
DOI: 10.58997/ejde.2020.122

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Jianlu Yan
Institute for Applied Mathematics
School of Mathematics
Southeast University
Nanjing 211189, China
email: 230159430@seu.edu.cn
Yuxiang Li
Institute for Applied Mathematics
School of Mathematics
Southeast University
Nanjing 211189, China
email: lieyx@seu.edu.cn

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