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arXiv · 1112.0269

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

Hector Giacomini·Armengol Gasull·Joan Torregrosa
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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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Hector Giacomini, Armengol Gasull, Joan Torregrosa. 2011-12-01. Explicit upper and lower bounds for the traveling wave solutions of Fisher-Kolmogorov type equations. https://arxiv.org/abs/1112.0269

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