Home > Articles > Published articles > Explicit upper and lower bounds for the traveling wave solutions of Fisher-Kolmogorov type equations |
Date: | 2013 |
Abstract: | It is well-known that the existence of traveling wave solutions for reaction-diffusion partial differential equations can be proved by showing the existence of certain heteroclinic orbits for related autonomous planar differential equations. We introduce a method for finding explicit upper and lower bounds of these heteroclinic orbits. In particular, for the classical Fisher-Kolmogorov equation we give rational upper and lower bounds which allow to locate these solutions analytically and with very high accuracy. |
Grants: | Ministerio de Ciencia y Tecnología MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 |
Rights: | Tots els drets reservats. |
Language: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Subject: | Traveling wave ; Heteroclinic orbit ; Fisher-Kolmogorov equation ; Reaction-diffusion partial differential equation ; Invariant manifold |
Published in: | Discrete and continuous dynamical systems. Series A, Vol. 33 Núm. 8 (2013) , p. 3567-3582, ISSN 1553-5231 |
Postprint 14 p, 421.0 KB |