杜宛娟.一类具有奇异灵敏度的logistic趋化系统解的渐近行为[J].数学研究及应用,2021,41(5):473~480 |
一类具有奇异灵敏度的logistic趋化系统解的渐近行为 |
Asymptotic Behavior of Solutions to a Logistic Chemotaxis System with Singular Sensitivity |
投稿时间:2020-09-07 修订日期:2021-01-03 |
DOI:10.3770/j.issn:2095-2651.2021.05.004 |
中文关键词: 渐近行为 趋化 奇异灵敏度 logistic源 |
英文关键词:asymptotic behavior chemotaxis singular sensitivity logistic source |
基金项目:西华师范大学创新团队项目(Grant No.CXTD2020-5),西华师范大学英才项目(Grant No.17YC372). |
|
摘要点击次数: 533 |
全文下载次数: 400 |
中文摘要: |
本文在无边界流的光滑有界区域$\Omega\subset\mathbb{R}^n~(n>2)$上研究了具有奇异灵敏度及logistic源的抛物-椭圆趋化系统$$\left\{\begin{array}{ll}u_t=\Delta u-\chi\nabla\cdot(\frac{u}{v}\nabla v)+r u-\mu u^k,&x\in\Omega,\,t>0,\\ 0=\Delta v-v+u,&x\in\Omega,\,t>0\end{array}\right.$$ 其中$\chi$, $r$, $\mu>0$, $k\geq2$. 证明了若当$r$适当大, 则当$t\rightarrow\infty$时该趋化系统全局有界解呈指数收敛于$((\frac{r}{\mu})^{\frac{1}{k-1}}, (\frac{r}{\mu})^{\frac{1}{k-1}})$. |
英文摘要: |
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. |
查看全文 查看/发表评论 下载PDF阅读器 |
|
|
|