Destabilisation of fronts in a class of bistable systems

Arjen Doelmant, David Iron, Yasumasa Nishiura

研究成果: Article査読

11 被引用数 (Scopus)

抄録

In this article, we consider a class of bistable reaction-diffusion equations in two components on the real line. We assume that the system is singularly perturbed, i.e., that the ratio of the diffusion coefficients is (asymptotically) small. This class admits front solutions that are asymptotically close to the (stable) front solution of the "trivial" scalar bistable limit system ut = uxx+u(1-u2). However, in the system these fronts can become unstable by varying parameters. This destabilization is caused by either the essential spectrum associated to the linearized stability problem or by an eigenvalue that exists near the essential spectrum. We use the Evans function to study the various bifurcation mechanisms and establish an explicit connection between the character of the destabilization and the possible appearance of saddle-node bifurcations of heteroclinic orbits in the existence problem.

本文言語English
ページ(範囲)1420-1450
ページ数31
ジャーナルSIAM Journal on Mathematical Analysis
35
6
DOI
出版ステータスPublished - 2004
外部発表はい

ASJC Scopus subject areas

  • 分析
  • 計算数学
  • 応用数学

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