Entire solutions for a discrete diffusive equation

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23 Citations (Scopus)

Abstract

We study entire solutions of a discrete diffusive equation with bistable nonlinearity. It is well known that there are three different wavefronts connecting any two of those three equilibria, say, 0, a, 1. We construct three different types of entire solutions. The first one is a solution which behaves as two opposite wavefronts (connecting 0 and 1) of the same positive speed approaching each other from both sides of the real line. The second one is a solution which behaves as two different wavefronts (connecting a and one of {0, 1}) approaching each other from both sides of the real line and converging to the wavefront connecting 0 and 1. The third one is a solution which behaves as a wavefront connecting a and 0 and a wavefront connecting 0 and 1 approaching each other from both sides of the real line.

Original languageEnglish
Pages (from-to)450-458
Number of pages9
JournalJournal of Mathematical Analysis and Applications
Volume347
Issue number2
DOIs
Publication statusPublished - 2008 Nov 15

Keywords

  • Asymptotic behavior
  • Discrete diffusive equation
  • Entire solution
  • Wavefront

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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