Keller-Segel Chemotaxis Models: A Review

被引：0
作者：
Gurusamy Arumugam
Jagmohan Tyagi
机构：
[1] Indian Institute of Technology Gandhinagar,Discipline of Mathematics
来源：
Acta Applicandae Mathematicae | 2021年 / 171卷
关键词：
Chemotaxis; Keller-Segel models; Weak solutions; Renormalized solutions; Local existence; Global existence; Blow-up; Boundedness; Stabilization; Asymptotic behavior of solutions; Finite difference method; Finite element method; Finite Volume method; Discontinuous Galerkin method; 35A01; 35D30; 35B44; 34H15; 35K40; 65N30; 65M08; 65M06;
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摘要：
We recount and discuss some of the most important methods and blow-up criteria for analyzing solutions of Keller-Segel chemotaxis models. First, we discuss the results concerning the global existence, boundedness and blow-up of solutions to parabolic-elliptic type models. Thereafter we describe the global existence, boundedness and blow-up of solutions to parabolic-parabolic models. The numerical analysis of these models is still at a rather early stage only. We recollect quite a few of the known results on numerical methods also and direct the attention to a number of open problems in this domain.
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