How does the spreading speed associated with the Fisher-KPP equation depend on random stationary diffusion and reaction terms? - Laboratoire Jacques-Louis Lions Accéder directement au contenu
Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series B Année : 2015

How does the spreading speed associated with the Fisher-KPP equation depend on random stationary diffusion and reaction terms?

Grégoire Nadin

Résumé

We consider one-dimensional reaction-diffusion equations of Fisher-KPP type with random stationary ergodic coefficients. A classical result of Freidlin and Gartner [16] yields that the solutions of the initial value problems associated with compactly supported initial data admit a linear spreading speed almost surely. We use in this paper a new characterization of this spreading speed recently proved in [8] in order to investigate the dependence of this speed with respect to the heterogeneity of the diffusion and reaction terms. We prove in particular that adding a reaction term with null average or rescaling the coefficients by the change of variables x → x/L, with L > 1, speeds up the propagation. From a modelling point of view, these results mean that adding some heterogeneity in the medium gives a higher invasion speed, while fragmentation of the medium slows down the invasion.
Fichier principal
Vignette du fichier
nadindeprevised.pdf (214 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01360594 , version 1 (06-09-2016)

Identifiants

Citer

Grégoire Nadin. How does the spreading speed associated with the Fisher-KPP equation depend on random stationary diffusion and reaction terms?. Discrete and Continuous Dynamical Systems - Series B, 2015, 20 (6), pp.1785-1803. ⟨10.3934/dcdsb.2015.20.1785⟩. ⟨hal-01360594⟩
371 Consultations
170 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More