NUMERICAL STUDY OF TWO-SPECIES CHEMOTAXIS MODELS

被引：31

作者：

Kurganov, Alexander ^{[1
]}

Lukacova-Medvidova, Maria ^{[2
]}

机构：

[1] Tulane Univ, Dept Math, New Orleans, LA 70118 USA

[2] Johannes Gutenberg Univ Mainz, Inst Math, D-55099 Mainz, Germany

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2014年 / 19卷 / 01期

基金：

美国国家科学基金会;

关键词：

Two-species chemotaxis models; second-order positivity preserving finite-volume method; finite-time blow-up; HYPERBOLIC CONSERVATION-LAWS; GLOBAL EXISTENCE; CONCENTRATION REGIONS; POINT DYNAMICS; SINGULAR LIMIT; BLOW-UP; STABILITY; SYSTEM; SCHEMES; FLUX;

D O I：

10.3934/dcdsb.2014.19.131

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We first conduct a comparative numerical study of two recently proposed two-species chemotaxis models. We show that different scenarios are possible: depending on the initial masses, either one or both cell densities may blow up, or a global solution may exist. In particular, our numerical results indicate answers on some open questions of possible blow up stated in [4,7]. We then introduce two regularizations of the studied models and demonstrate that their solutions are capable of developing spiky structure without blowing up.

引用

页码：131 / 152

页数：22

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