Turing instability analysis of a singular cross-diffusion problem

Electronic Journal of Differential Equations

article

Gonzalo Galiano¹  Víctor González-Tabernero² 

[1] Department of Mathematics University of Oviedo Oviedo;Department of Mathematics University of Santiago de Compostela Santiago de Compostela

关键词: Cross-diffusion;    Turing instability;    weakly nonlinear equation;    finite element method.;   

DOI  :  10.58997/ejde.2021.55

学科分类：数学（综合）

来源: Texas State University

【 摘 要 】

The population model by Busenberg and Travis is a paradigmatic model in ecologyand tumor modeling because its ability to capture interesting phenomenasuch as segregation of populations. Its singular mathematical structure enforcesthe consideration of regularized problems to deduce properties as fundamentalas the existence of solutions.In this article we perform a weakly nonlinear stability analysis of a generalclass of regularized problems to study the convergence of the instability modesin the limit of the regularization parameter. We demonstrate with some specificexamples that the pattern formation observed in the regularized problems,with unbounded wave numbers, is not present in the limit problem because of theamplitude decay of the oscillations.We also check the results of the stability analysis with direct finite elementsimulations of the problem.

【 授权许可】

CC BY