Traveling waves in a one-dimensional random medium

2007/10/09 by James Nolen, Nolen, James, Lenya Ryzhik +1
Mathematics · Medicine · #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.0710.1858

openalex publication_date 2007/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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