On the Structure of Multiple Existence of Stable Stationary Solutions in Systems of Reaction-Diffusion Equations

Hiroshi Fujii, Yasumasa Nishiura, Yuzo Hosono

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

This article is intended to survey the results about pattern formation in a class of reaction-diffusion systems. The focus is on the phenomenon of multiple existence of stable stationary solutions, which has biologically or physically significant consequences. The mathematical structure and stability of stationary solutions is investigated in a certain parameter space. Especially, σ-local stability and instability theorems for D1-sheet are given, and stabilization of D2-sheet is proved via two approaches: the spectral method and the singular perturbation-theoretic one.

Original languageEnglish
Pages (from-to)157-219
Number of pages63
JournalStudies in Mathematics and its Applications
Volume18
Issue numberC
DOIs
Publication statusPublished - 1986 Jan 1

Keywords

  • bifurcation
  • pattern formation
  • reaction-diffusion
  • singular perturbation
  • stability

ASJC Scopus subject areas

  • Applied Mathematics

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