Explicit upper and lower bounds for the traveling wave solutions of Fisher-Kolmogorov type equations
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Giacomini, Hector (Université de Tours(France). Laboratoire de Mathématiques et Physique Théorique)

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

DOI: 10.3934/dcds.2013.33.3567

Postprint 14 p, 421.0 KB

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