English

Traveling waves in a one-dimensional random medium

Analysis of PDEs 2007-10-10 v1 Probability

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.

Keywords

Cite

@article{arxiv.0710.1858,
  title  = {Traveling waves in a one-dimensional random medium},
  author = {James Nolen and Lenya Ryzhik},
  journal= {arXiv preprint arXiv:0710.1858},
  year   = {2007}
}

Comments

27 pages

R2 v1 2026-06-21T09:29:18.773Z