Transversal instability for the thermodiffusive reaction-diffusion system - Laboratoire Jacques-Louis Lions Accéder directement au contenu
Article Dans Une Revue Chinese Annals of Mathematics - Series B Année : 2015

Transversal instability for the thermodiffusive reaction-diffusion system

Résumé

The propagation of unstable interfaces is at the origin of remarkable patterns that are observed in various areas of science as chemical reactions, phase transitions, growth of bacterial colonies. Since a scalar equation generates usually stable waves, the simplest mathematical description relies on two by two reaction-diffusion systems. Our interest is the extension of the Fisher/KPP equation to a two species reaction which represents reactant concentration and temperature when used for flame propagation, bacterial population and nutrient concentration when used in biology. We study in which circumstances instabilities can occur and in particular the effect of dimension. It is observed numerically that spherical waves can be unstable depending on the coefficients. A simpler mathematical framework is to study transversal instability, that means a one dimensional wave propagating in two space dimensions. Then, explicit analytical formulas give explicitely the range of paramaters for instability.
Fichier principal
Vignette du fichier
instab_v3.pdf (869.23 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00939013 , version 1 (29-01-2014)

Identifiants

Citer

Michal Kolwalczyk, Benoît Perthame, Nicolas Vauchelet. Transversal instability for the thermodiffusive reaction-diffusion system. Chinese Annals of Mathematics - Series B, 2015, 36 (5), pp.871-882. ⟨10.1007/s11401-015-0981-x⟩. ⟨hal-00939013⟩
386 Consultations
209 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More