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

2011/12/01 by Hector Giacomini, Armengol Gasull, Giacomini, Hector +3
Mathematics · #34C37 (Primary) 35C07 #37C29 (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:34C37 #msc:35C07 #msc:37C29

paper · pdf · doi:10.48550/arxiv.1112.0269

14 pages, 7 figures

arxiv created 2011/12/01 · arxiv updated 2011/12/02

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.

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