article

Title: A viscosity solution method for the spreading speed formula in slowly varying media

Authors: Francois Hamel, Gregoire Nadin and Lionel Roques

Issue: Volume 60 (2011), Issue 4, 1229-1248

Abstract:

In this paper, we consider reaction-diffusion-advection equations in slowly periodically oscillating media. We prove the existence of and give explicit expressions of the asymptotic spreading speeds of invasion of the unstable state $0$ in any direction, when the period of the invaded medium becomes infinitely large. The limiting spreading speeds involve families of $1$-periodic Hamilton-Jacobi equations. In the case of one-dimensional reaction-diffusion equations, we analyze the relative effects of small perturbations of the diffusion and the reaction coefficients, and we compare the spreading speeds in slowly oscillating media to the homogenized spreading speeds in rapidly oscillating media.