Communications on Pure and Applied Analysis (CPAA)

Instability of multi-spot patterns in shadow systems of reaction-diffusion equations

Pages: 717 - 736, Volume 14, Issue 2, March 2015      doi:10.3934/cpaa.2015.14.717

       Abstract        References        Full Text (578.7K)       Related Articles       

Shin-Ichiro Ei - Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo, 060-0810, Japan (email)
Kota Ikeda - Department of Mathematical Sciences Based on Modeling and Analysis, Meiji University, Nakano-ku, Tokyo, 164-8525, Japan (email)
Eiji Yanagida - Department of Mathematics, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8551, Japan (email)

Abstract: Our aim in this paper is to prove the instability of multi-spot patterns in a shadow system, which is obtained as a limiting system of a reaction-diffusion model as one of the diffusion coefficients goes to infinity. Instead of investigating each eigenfunction for a linearized operator, we characterize the eigenspace spanned by unstable eigenfunctions.

Keywords:  Eigenpair, multi-spot solution, shadow system, reaction-diffusion equation, stability
Mathematics Subject Classification:  Primary: 35B36, 35K57; Secondary: 37L15

Received: July 2013;      Revised: December 2013;      Available Online: December 2014.