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. 1021–1047DOI 10.1016/J.ANIHPC.2009.02.003