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

Shin-Ichiro Ei; Kota Ikeda; Eiji Yanagida

doi:10.3934/cpaa.2015.14.717

Article Contents

2015, Volume 14, Issue 2: 717-736. Doi: 10.3934/cpaa.2015.14.717

This issue Previous Article Regularity of the attractor for a coupled Klein-Gordon-Schrödinger system with cubic nonlinearities in $\mathbb{R}^2$ Next Article Corrigendum of "Local well-posedness for the nonlinear Dirac equation in two space dimensions"

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

1.
Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo, 060-0810
2.
Department of Mathematical Sciences Based on Modeling and Analysis, Meiji University, Nakano-ku, Tokyo, 164-8525
3.
Department of Mathematics, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8551

Received: June 30, 2013

Revised: November 30, 2013

Published: February 2015

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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.

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Mathematics Subject Classification: Primary: 35B36, 35K57; Secondary: 37L15.

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