论文标题
涉及张量值敏感性和罗宾型边界条件的趋化性消费系统的常规溶液
Regular solutions of chemotaxis-consumption systems involving tensor-valued sensitivities and Robin type boundary conditions
论文作者
论文摘要
本文涉及带有张量值的灵敏度$ s（x，n，c）$的抛物线纤维化趋化性系统，在$ n $和$ c $的robin型边界条件下。有限的经典解决方案的全球存在是在张张值敏感性$ s $的一般假设下以二维为准建立的。主要步骤之一是证明$ \ nabla c（\ cdot，t）$在$ l^{2}（b_ {r}（x）（x）（x）\capΩ）$中，对于每个$ x \ in \overlineΩ$和$ t $时，$ r $当$ r $很小，这似乎是独立的，这是独立的利益。另一方面，在标量值的灵敏度$ s =χ（x，n，c）\ mathbb {i} $的情况下，在两个及更高维度的全球范围内存在一个有界的经典解决方案，前提是该域是一个radius $ r $的球，并且所有给定的数据都是径向的。径向盒的结果涵盖了标量值敏感性$χ$，在$ c = 0 $时可能是单数。
This paper deals with a parabolic-elliptic chemotaxis-consumption system with tensor-valued sensitivity $S(x,n,c)$ under no-flux boundary conditions for $n$ and Robin-type boundary conditions for $c$. The global existence of bounded classical solutions is established in dimension two under general assumptions on tensor-valued sensitivity $S$. One of main steps is to show that $\nabla c(\cdot,t)$ becomes tiny in $L^{2}(B_{r}(x)\cap Ω)$ for every $x\in\overlineΩ$ and $t$ when $r$ is sufficiently small, which seems to be of independent interest. On the other hand, in the case of scalar-valued sensitivity $S=χ(x,n,c)\mathbb{I}$, there exists a bounded classical solution globally in time for two and higher dimensions provided the domain is a ball with radius $R$ and all given data are radial. The result of the radial case covers scalar-valued sensitivity $χ$ that can be singular at $c=0$.
