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

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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https://hal.archives-ouvertes.fr/hal-00784560
Contributor : Hector Giacomini <>
Submitted on : Monday, February 4, 2013 - 2:17:31 PM
Last modification on : Thursday, March 5, 2020 - 5:33:25 PM

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Hector Giacomini, Armengol Gasull, Joan Torregrosa. Explicit upper and lower bounds for the traveling wave solutions of Fisher-Kolmogorov type equations. Discrete and Continuous Dynamical Systems - Series A, American Institute of Mathematical Sciences, 2013, 33, pp.3567 - 3582. ⟨10.3934/dcds.2013.33.3567⟩. ⟨hal-00784560⟩

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