Entire solutions for a discrete diffusive equation

• Published in: Journal of mathematical analysis and applications Vol. 347; no. 2; pp. 450 - 458
• Main Author: Guo, Yung-Jen Lin
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 15.11.2008; Elsevier
• Subjects: Asymptotic behavior; Discrete diffusive equation; Entire solution; Exact sciences and technology; Mathematical analysis; Mathematics; Sciences and techniques of general use; Wavefront; Entire solution; Discrete diffusive equation; Asymptotic behavior; Wavefront; Entire solution;Discrete diffusive equation;Wavefront;Asymptotic behavior; Nonlinearity; Mathematical analysis; Application
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2008.03.076

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.