Traveling waves in a one-dimensional heterogeneous medium

James Nolen; Lenya Ryzhik

doi:10.1016/j.anihpc.2009.02.003

JournalsaihpcVol. 26, No. 3pp. 1021–1047

Traveling waves in a one-dimensional heterogeneous medium

James Nolen
Department of Mathematics, Stanford University, Stanford, CA 94305, USA
- MathSciNet
- zbMATH Open
Lenya Ryzhik
Department of Mathematics, University of Chicago, Chicago, IL 60637, USA
- MathSciNet
- zbMATH Open

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Abstract

We consider solutions of a scalar reaction–diffusion equation of the ignition type with a random, stationary and ergodic reaction rate. We show that solutions of the Cauchy problem spread with a deterministic rate in the long time limit. We also establish existence of generalized random traveling waves and of transition fronts in general heterogeneous media.

Cite this article

James Nolen, Lenya Ryzhik, Traveling waves in a one-dimensional heterogeneous medium. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 3, pp. 1021–1047

DOI 10.1016/J.ANIHPC.2009.02.003