Explicit upper and lower bounds for the traveling wave solutions of Fisher-Kolmogorov type equations

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...

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Detalles Bibliográficos
Autores: Gasull, Armengol|||0000-0002-1719-8231, Torregrosa, Joan|||0000-0002-2753-1827, Giacomini, Hector
Tipo de recurso: artículo
Fecha de publicación:2013
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:150651
Acceso en línea:https://ddd.uab.cat/record/150651
https://dx.doi.org/urn:doi:10.3934/dcds.2013.33.3567
Access Level:acceso abierto
Palabra clave:Traveling wave
Heteroclinic orbit
Fisher-Kolmogorov equation
Reaction-diffusion partial differential equation
Invariant manifold
Descripción
Sumario: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.