论文标题
在非线性Neumann边界条件下具有逻辑源的趋化系统解决方案的全球存在
Global existence of solutions to the chemotaxis system with logistic source under nonlinear Neumann boundary condition
论文作者
论文摘要
我们考虑具有逻辑来源$ f（u）的趋化系统的经典解决方案：= au-μu^2 $在非线性neumann边界条件下$ \ frac {\ partial u} {\ partial u} {\ partialν} = | u | u |^{p} $ with $ p> in $ p> $ p>在平滑的convex bounded domain $ p>中，$ p> n $ p> n $ n $ p> n $ p> n $ p> n n $ n $ p> n $ \ geq 2 $。本文的目的是表明，如果$ p <\ frac {3} {2} $和$μ> 0 $，$ n = 2 $或$μ$在$ n \ geq 3 $时就足够大，那么抛物线式推着层次化趋化性趋化趋化性系统将承认一个独特的积极的全球经典解决方案，该解决方案在$ phime $ phime by in $ philes（0）中，$ cheftty（0）。如果$ p <\ frac {3} {2} $，$ n = 2 $，而$μ> 0 $> 0 $或$ p <\ frac {7} {7} {5} $，$ n = 3 $，而$μ$也足够大，那么类似的结果也是正确的。
We consider classical solutions to the chemotaxis system with logistic source $f(u) := au-μu^2$ under nonlinear Neumann boundary condition $\frac{\partial u}{ \partial ν} = |u|^{p}$ with $p>1$ in a smooth convex bounded domain $Ω\subset \mathbb{R}^n$ where $n \geq 2$. This paper aims to show that if $p<\frac{3}{2}$, and $μ>0$, $n=2$, or $μ$ is sufficiently large when $n\geq 3$, then the parabolic-elliptic chemotaxis system admits a unique positive global-in-time classical solution that is bounded in $Ω\times (0, \infty)$. The similar result is also true if $p<\frac{3}{2}$, $n=2$, and $μ>0$ or $p<\frac{7}{5}$, $n=3$, and $μ$ is sufficiently large for the parabolic-parabolic chemotaxis system.
