A viscosity solution method for the spreading speed formula in slowly varying media - Sorbonne Université Access content directly
Journal Articles Indiana University Mathematics Journal Year : 2011

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

François Hamel
Grégoire Nadin
Lionel Roques

Abstract

In this paper, we consider reaction-diffusion-advection equations in slowly periodi-cally oscillating media. We prove the existence of and we 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 sprea-ding 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.
Fichier principal
Vignette du fichier
hnr3 (1).pdf (208.41 Ko) Télécharger le fichier
Origin Files produced by the author(s)
Loading...

Dates and versions

hal-01080131 , version 1 (01-03-2016)

Identifiers

Cite

François Hamel, Grégoire Nadin, Lionel Roques. A viscosity solution method for the spreading speed formula in slowly varying media. Indiana University Mathematics Journal, 2011, 60 (4), pp.1229 - 1248. ⟨10.1512/iumj.2011.60.4370⟩. ⟨hal-01080131⟩
195 View
182 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More