Article
MSC:
35A01,
35B40,
35B45,
35K60,
35M33,
92C17 | MR 3306853 | Zbl 06433687 | DOI: 10.21136/MB.2014.144140
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Keywords:
chemotaxis; global existence; boundedness
chemotaxis; global existence; boundedness
Summary:
This paper deals with parabolic-elliptic chemotaxis systems with the sensitivity function $\chi (v)$ and the growth term $f(u)$ under homogeneous Neumann boundary conditions in a smooth bounded domain. Here it is assumed that $0< \chi (v)\leq {{\chi }_0}/{v^k}$ $(k\geq 1$, ${\chi }_0>0)$ and $\lambda _1-\mu _1 u \leq f(u)\leq \lambda _2-\mu _2 u$ $(\lambda _1,\lambda _2,\mu _1,\mu _2>0)$. It is shown that if $\chi _0$ is sufficiently small, then the system has a unique global-in-time classical solution that is uniformly bounded. This boundedness result is a generalization of a recent result by K. Fujie, M. Winkler, T. Yokota.
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