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January  2010, 26(1): 303-312. doi: 10.3934/dcds.2010.26.303

Generalized fronts for one-dimensional reaction-diffusion equations

Antoine Mellet 1, , Jean-Michel Roquejoffre 2, and  Yannick Sire 3,

1. 

Department of Mathematics, University of Maryland, College Park, MD 20742, United States
2. 

Institut de Mathématiques, Université Paul Sabatier, F-31062 Toulouse, France
3. 

LATP, Université Aix-Marseille III, F-13397 Marseille, France

Received  January 2009 Revised  May 2009 Published  October 2009

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.
Keywords: Fronts propagation, Reaction-diffusion equations, Heterogeneous media..
Mathematics Subject Classification: Primary: 35K5.
Citation: Antoine Mellet, Jean-Michel Roquejoffre, Yannick Sire. Generalized fronts for one-dimensional reaction-diffusion equations. Discrete & Continuous Dynamical Systems, 2010, 26 (1) : 303-312. doi: 10.3934/dcds.2010.26.303
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