Asymptotic Behavior of Solutions to a Logistic Chemotaxis System with Singular Sensitivity
Received:September 07, 2020  Revised:January 03, 2021
Key Words: asymptotic behavior   chemotaxis   singular sensitivity   logistic source  
Fund Project:Supported by Innovation Team of China West Normal University (Grant No.CXTD2020-5) and the Meritocracy Research Funds of China West Normal University (Grant No.17YC372).
Author NameAffiliation
Wanjuan DU Institute for Advanced Studies in the History of Science, Northwest University, Shaanxi 710217, P. R. China
College of Mathematics Education, China West Normal University, Sichuan 637009, P. R. China 
Hits: 484
Download times: 357
Abstract:
      In this paper, we study the asymptotic behavior of solutions to the parabolic-elliptic chemotaxis system with singular sensitivity and logistic source $$\left\{\begin{array}{ll}u_t=\Delta u-\chi\nabla\cdot(\frac{u}{v}\nabla v)+r u-\mu u^k,&x\in\Omega,\,t>0,\\ 0=\Delta v-v+u,&x\in\Omega,\,t>0\end{array}\right.$$ in a smooth bounded domain $\Omega\subset\mathbb{R}^n~(n>2)$ with the non-flux boundary, where $\chi$, $r$, $\mu>0$, $k\geq2$. It is proved that the global bounded classical solution will exponentially converge to $((\frac{r}{\mu})^{\frac{1}{k-1}}, (\frac{r}{\mu})^{\frac{1}{k-1}})$ as $t\rightarrow\infty$ if $r$ is suitably large.
Citation:
DOI:10.3770/j.issn:2095-2651.2021.05.004
View Full Text  View/Add Comment