Entire solutions for a discrete diffusive equation

Yung Jen Lin Guo

doi:10.1016/j.jmaa.2008.03.076

Entire solutions for a discrete diffusive equation

Yung Jen Lin Guo^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

27 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
Pages (from-to)	450-458
Number of pages	9
Journal	Journal of Mathematical Analysis and Applications
Volume	347
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2008.03.076
Publication status	Published - 2008 Nov 15

Keywords

Asymptotic behavior
Discrete diffusive equation
Entire solution
Wavefront

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2008.03.076

Cite this

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title = "Entire solutions for a discrete diffusive equation",

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.",

keywords = "Asymptotic behavior, Discrete diffusive equation, Entire solution, Wavefront",

author = "Guo, {Yung Jen Lin}",

note = "Funding Information: This work was partially supported by the National Science Council of the Republic of China under the grant NSC 94-2115-M-003-009. E-mail address: [email protected].",

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AU - Guo, Yung Jen Lin

N1 - Funding Information: This work was partially supported by the National Science Council of the Republic of China under the grant NSC 94-2115-M-003-009. E-mail address: [email protected].

PY - 2008/11/15

Y1 - 2008/11/15

N2 - 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.

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.

KW - Asymptotic behavior

KW - Discrete diffusive equation

KW - Entire solution

KW - Wavefront

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Entire solutions for a discrete diffusive equation

Abstract

Keywords

ASJC Scopus subject areas

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