| Title:
|
Boundedness in a fully parabolic chemotaxis system with signal-dependent sensitivity and logistic term (English) |
| Author:
|
Mizukami, Masaaki |
| Language:
|
English |
| Journal:
|
Proceedings of Equadiff 14 |
| Volume:
|
Conference on Differential Equations and Their Applications, Bratislava, July 24-28, 2017 |
| Issue:
|
2017 |
| Year:
|
|
| Pages:
|
61-68 |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper deals with the chemotaxis system with signal-dependent sensitivity and logistic term \begin{align*} &u_t=\Delta u - \nabla \cdot (u \chi(v)\nabla v) + \mu u(1-u), % \quad \\ &v_t=\Delta v + u - v \end{align*} in $\Omega\times (0,\infty)$, where $\Omega$ is a bounded domain in $\mathbb{R}^n$ ($n\ge 2$) with smooth boundary, $\mu > 0$ is a constant and $\chi$ is a function generalizing \begin{align*} \chi(s) = \frac{K}{(1+s)^2} \quad (K>0,\ s>0). \end{align*} In the case that $\mu=0$ global existence and boundedness were established under some conditions for global existence and boundedness in the above system.([14]); however, conditions for global existence and boundedness in the above system have not been studied. The purpose of this paper is to construct conditions for global existence and boundedness in the above system. (English) |
| Keyword:
|
Chemotaxis; signal-dependent sensitivity; logistic term; global existence. |
| MSC:
|
35A01 |
| MSC:
|
35K51 |
| MSC:
|
92C17. |
| . |
| Date available:
|
2019-09-27T07:39:40Z |
| Last updated:
|
2019-09-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/703018 |
| . |
| Reference:
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