有界函数
数学
饱和(图论)
趋化性
扩散
数学分析
边值问题
多孔介质
边界(拓扑)
类型(生物学)
多孔性
物理
化学
组合数学
热力学
生物
生物化学
受体
有机化学
生态学
作者
Chunyan Wu,Zhaoyin Xiang
标识
DOI:10.1016/j.jde.2022.01.033
摘要
In this paper, we investigate a chemotaxis-Stokes system with porous-media type cell diffusion ∇⋅(nm−1∇n) in a bounded domain Ω⊂RN (N=2,3) with smooth boundary. We prove that for the no-flux–saturation–no-slip boundary value and suitable regular initial data, the mild assumption m>3N−22N is sufficient for the global existence and boundedness of weak solutions, and in particular confirm the experimental observation in Tuval et al. (2005, PNAS). In comparison to the considerable literature, the novelty here is that we require signal to attain a prescribed saturation value throughout the boundary. This result will be the first step towards a qualitative theory for the boundary layer.
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