Advanced Studies in Pure Mathematics

Stability analysis for a stripe solution in the Gierer-Meinhardt system

Kota Ikeda

Full-text: Open access

Abstract

We consider the Gierer-Meinhardt system on a rectangle in two-dimensional space. This system is considered to generate some spiky pattern for a wide range of parameters. On a rectangle, this system also has a stripe solution, which is known to be unstable from numerical results. In this paper, we show the instability of the stripe pattern in a mathematically rigorous manner by using the SLEP method.

Article information

Source
Asymptotic Analysis and Singularities — Elliptic and parabolic PDEs and related problems, H. Kozono, T. Ogawa, K. Tanaka, Y. Tsutsumi and E. Yanagida, eds. (Tokyo: Mathematical Society of Japan, 2007), 573-587

Dates
Received: 13 November 2005
Revised: 11 January 2006
First available in Project Euclid: 16 December 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1545000894

Digital Object Identifier
doi:10.2969/aspm/04720573

Mathematical Reviews number (MathSciNet)
MR2387256

Zentralblatt MATH identifier
1144.35397

Citation

Ikeda, Kota. Stability analysis for a stripe solution in the Gierer-Meinhardt system. Asymptotic Analysis and Singularities — Elliptic and parabolic PDEs and related problems, 573--587, Mathematical Society of Japan, Tokyo, Japan, 2007. doi:10.2969/aspm/04720573. https://projecteuclid.org/euclid.aspm/1545000894


Export citation