ALFARO, Matthieu; DUCROT, Arnaud; GILETTI, Thomas

doi:10.1112/plms.12092

Métadonnées

Afficher la notice complète

Licence d’utilisation du document

ALFARO, Matthieu
Institut Montpelliérain Alexander Grothendieck [IMAG]

DUCROT, Arnaud
Institut de Mathématiques de Bordeaux [IMB]

GILETTI, Thomas
Institut Élie Cartan de Lorraine [IECL]

Langue

Article de revue

Ce document a été publié dans

Proceedings of the London Mathematical Society. 2018, vol. 116, n° 4, p. 729-759

London Mathematical Society

Résumé en anglais

We consider a bistable ($0<\theta<1$ being the three constant steady states) delayed reaction diffusion equation, which serves as a model in population dynamics. The problem does not admit any comparison principle. This prevents the use of classical technics and, as a consequence, it is far from obvious to understand the behaviour of a possible travelling wave in $+\infty$. Combining refined {\it a priori} estimates and a Leray Schauder topological degree argument, we construct a travelling wave connecting 0 in $-\infty$ to \lq\lq something'' which is strictly above the unstable equilibrium $\theta$ in $+\infty$. Furthemore, we present situations (additional bound on the nonlinearity or small delay) where the wave converges to 1 in $+\infty$, whereas the wave is shown to oscillate around 1 in $+\infty$ when, typically, the delay is large.< Réduire

Métadonnées

Partager cette publication !

Licence d’utilisation du document

Travelling waves for a non-monotone bistable equation with delay: existence and oscillations

Langue

Ce document a été publié dans

Résumé en anglais

URI

DOI

Origine

Unités de recherche