Generalized fronts for one-dimensional reaction-diffusion equations

Antoine Mellet; Jean-Michel Roquejoffre; Yannick Sire

doi:10.3934/dcds.2010.26.303

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2010, Volume 26, Issue 1: 303-312. Doi: 10.3934/dcds.2010.26.303

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Generalized fronts for one-dimensional reaction-diffusion equations

1.
Department of Mathematics, University of Maryland, College Park, MD 20742
2.
Institut de Mathématiques, Université Paul Sabatier, F-31062 Toulouse
3.
LATP, Université Aix-Marseille III, F-13397 Marseille

Received: December 31, 2008

Revised: April 30, 2009

Published: February 2010

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Abstract

For a class of one-dimensional reaction-diffusion equations, we establish the existence of generalized fronts, as recently defined by Berestycki and Hamel. We also prove uniform nondegeneracy estimates, such as a lower bound on the time derivative on some level sets, as well as a lower bound on the spatial derivative.

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Mathematics Subject Classification: Primary: 35K57.

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