抛物-椭圆吸引排斥趋化模型的定性分析

Qualitative analysis of a parabolic-elliptic attraction-repulsion chemotaxis model

考虑一个抛物-椭圆吸引排斥趋化模型.通过建立合适的熵不等式,利用不动点原理,Lp估计技巧,广义的Gagliardo-Nirenberg插值不等式和Moser迭代,证明了当细胞的初始质量满足条件‖u0‖L1(Ω)≤xαCNG时,该模型存在惟一的整体解.

A parabolic-elliptic attraction-repulsion chemotaxis model is considered. By establishing appro- priate entropy inequality,based on a fixed point argument, LP-estimate technique,the generalized Gagli- ardo-Nirenberg inequality and Moser＇s iteration, it is proved that the model admits a unique global solu- tion provided the initial cell mass satisfies the condition that ｜｜U0｜｜L2（Ω）≤xaCNG.