Multiple stable patterns for some reaction-diffusion equation in disrupted environments

Takanori Ide, Kazuhiro Kurata, Kazunaga Tanaka

Research output: Contribution to journalArticle

Abstract

We study the existence of multiple positive stable solutions for -ε2Δu(x) = u(x)2(b(x) - u(x)) in Ω, ∂u/∂n(x) = 0 on ∂Ω. Here ε > 0 is a small parameter and b(x) is a piecewise continuous function which changes sign. These type of equations appear in a population growth model of species with a saturation effect in biology.

Original languageEnglish
Pages (from-to)93-116
Number of pages24
JournalDiscrete and Continuous Dynamical Systems
Volume14
Issue number1
DOIs
Publication statusPublished - 2006 Jan 1

Keywords

  • Nonlinear elliptic equations
  • Pattern formation
  • Singular perturbation
  • Stable solutions
  • Variational methods

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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