Geodesic
Boundedness of solutions to parabolic-elliptic chemotaxis-growth systems with signal-dependent sensitivity
Mathematica Bohemica, Tome 139 (2014) no. 4, pp. 639-647

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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.
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.
DOI : 10.21136/MB.2014.144140
Classification : 35A01, 35B40, 35B45, 35K60, 35M33, 92C17
Keywords: chemotaxis; global existence; boundedness 
Fujie, Kentarou; Yokota, Tomomi. Boundedness of solutions to parabolic-elliptic chemotaxis-growth systems with signal-dependent sensitivity. Mathematica Bohemica, Tome 139 (2014) no. 4, pp. 639-647. doi: 10.21136/MB.2014.144140
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