Traveling waves in a one-dimensional heterogeneous medium

  • James Nolen

    Department of Mathematics, Stanford University, Stanford, CA 94305, USA
  • Lenya Ryzhik

    Department of Mathematics, University of Chicago, Chicago, IL 60637, USA


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