论文标题
对具有奇异灵敏度的逻辑趋化系统的界限
Boundedness to a logistic chemotaxis system with singular sensitivity
论文作者
论文摘要
在本文中，我们研究具有奇异灵敏度和逻辑类型来源的抛物线弹性凯勒 - 塞格系统：$ u_t =ΔU-χ\ nabla \ nabla \ cdot（\ frac {u} {u} {u} {v} {v} {v} \ nabla v） $ω\ subset \ mathbb {r}^n $，$χ，r，μ> 0 $，$ k> 1 $和$ n \ ge 2 $。结果表明，如果$ k> \ frac {3n-2} {n} $和$ r> \ frac {χ^2} {4} $对于$ 0 <χ\ le 2 $，或$ r>χ-1$ for $χ> 2 $，则系统具有全球界限的经典解决方案。此外，在$ r，χ$的同一条件下，该系统在$ k \ in（2- \ frac {1} {n} {n}，\ frac {3n-2} {n}] $中时，该系统在全球通用解决方案中，此外，该全局广义解决方案应提供全球范围的全球范围，应提供$ \ \ \ frac {R} r} r} $ $ $ $ $ $ $ u__ $ u_ $ u_ 0 $ u_ 0 $ u_0 $ u_0 $ u_0 $ u_0 $ u_0 $ u_0 $ u_0 $ u_0 $ u_0 $ u_0 $ u_0 $ u_0 $ u_0 $ u_0 $ u_0 $ u_0 $ u_0 $ u_0 $ u_0。
In this paper, we study the parabolic-elliptic Keller-Segel system with singular sensitivity and logistic-type source: $ u_t=Δu-χ\nabla\cdot(\frac{u}{v}\nabla v)+ru-μu^k$, $0=Δv-v+u$ under the non-flux boundary conditions in a smooth bounded convex domain $Ω\subset\mathbb{R}^n$, $χ,r,μ>0$, $k>1$ and $n\ge 2$. It is shown that the system possesses a globally bounded classical solution if $k>\frac{3n-2}{n}$, and $r>\frac{χ^2}{4}$ for $0<χ\le 2$, or $r> χ-1$ for $χ>2$. In addition, under the same condition for $r,χ$, the system admits a global generalized solution when $k\in(2-\frac{1}{n},\frac{3n-2}{n}]$, moreover this global generalized solution should be globally bounded provided $\frac{r}μ$ and the initial data $u_0$ suitably small.
