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February  2009, 25(1): 89-108. doi: 10.3934/dcds.2009.25.89

Traveling wave speeds in rapidly oscillating media

Fathi Dkhil 1, and  Angela Stevens 2,

1. 

Département de Mathématiques, Institut Supérieur d'Informatique, Université Tunis El-Manar, 2 rue Abou Raihan Bayrouni, 2080 Ariana, Tunisia
2. 

Universität Heidelberg, Angewandte Mathematik und BioQuant, INF 267, D-69120 Heidelberg, Germany

Received  October 2007 Revised  September 2008 Published  June 2009

In this paper we study the effects of periodically varying heterogeneous media on the speed of traveling waves in reaction-diffusion equations. Under suitable conditions the traveling wave speed of the non-homogenized problem can be calculated in terms of the speed of the homogenized problem. We discuss a variety of examples and focus especially on the influence of the symmetric and antisymmetric part of the diffusion matrix on the wave speed.
Keywords: Reaction-diffusion equations, homogenization, traveling wave speed..
Mathematics Subject Classification: 35B20, 35B27, 35B50, 35C20, 35K55, 35K57, 41A6.
Citation: Fathi Dkhil, Angela Stevens. Traveling wave speeds in rapidly oscillating media. Discrete & Continuous Dynamical Systems, 2009, 25 (1) : 89-108. doi: 10.3934/dcds.2009.25.89
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