# Entire solutions for a discrete diffusive equation

Research output: Contribution to journalArticle

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 language English 450-458 9 Journal of Mathematical Analysis and Applications 347 2 https://doi.org/10.1016/j.jmaa.2008.03.076 Published - 2008 Nov 15

Entire Solution
Wavefronts
Wave Front
Real Line
Nonlinearity

### Keywords

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

### ASJC Scopus subject areas

• Analysis
• Applied Mathematics

### Cite this

In: Journal of Mathematical Analysis and Applications, Vol. 347, No. 2, 15.11.2008, p. 450-458.

Research output: Contribution to journalArticle

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AB - 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.

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