欧米茄
组合数学
Neumann边界条件
有界函数
边界(拓扑)
物理
正多边形
同种类的
数学物理
数学分析
数学
几何学
量子力学
作者
Abdelhakam Hassan Mohammed,Ali. B. B. Almurad
标识
DOI:10.30538/psrp-oma2022.0116
摘要
This paper deals with nonnegative solutions of the Neumann initial-boundary value problem for an attraction-repulsion chemotaxis model with logistic source term of Equation 1 in bounded convex domains \(\Omega\subset\mathbb{R}^{n},~ n\geq1\), with smooth boundary. It is shown that if the ratio \(\frac{\mu}{\chi \alpha-\xi \gamma}\) is sufficiently large, then the unique nontrivial spatially homogeneous equilibrium given by \((u_{1},u_{2},u_{3})=(1,~\frac{\alpha}{\beta},~\frac{\gamma}{\eta})\) is globally asymptotically stable in the sense that for any choice of suitably regular nonnegative initial data \((u_{10},u_{20},u_{30})\) such that \(u_{10}\not\equiv0\), the above problem possesses uniquely determined global classical solution \((u_{1},u_{2},u_{3})\) with \((u_{1},u_{2},u_{3})|_{t=0}=(u_{10},u_{20},u_{30})\) which satisfies $$\|u_{1}(\cdot,t)-1\|_{L^{\infty}(\Omega)}\rightarrow{0},~~ \|u_{2}(\cdot,t)-\frac{\alpha}{\beta}\|_{L^{\infty}(\Omega)}\rightarrow{0},~~ \|u_{3}(\cdot,t)-\frac{\gamma}{\eta}\|_{L^{\infty}(\Omega)}\rightarrow{0}.$$ \(\mathrm{as}~t\rightarrow{\infty}\).
科研通智能强力驱动
Strongly Powered by AbleSci AI