Propagation or extinction in bistable equations: the non-monotone role of initial fragmentation - CNRS - Centre national de la recherche scientifique Accéder directement au contenu
Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series S Année : 2024

Propagation or extinction in bistable equations: the non-monotone role of initial fragmentation

Résumé

In this paper, we investigate the large-time behavior of bounded solutions of the Cauchy problem for a reaction-diffusion equation in $\mathbb{R}^N$ with bistable reaction term. We consider initial conditions that are chiefly indicator functions of bounded Borel sets. We examine how geometric transformations of the supports of these initial conditions affect the propagation or extinction of the solutions at large time. We also consider two fragmentation indices defined in the set of bounded Borel sets and we establish some propagation or extinction results when the initial supports are weakly or highly fragmented. Lastly, we show that the large-time dynamics of the solutions is not monotone with respect to the considered fragmentation indices, even for equimeasurable sets.
Fichier principal
Vignette du fichier
ahr.pdf (832.06 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04055502 , version 1 (02-04-2023)

Identifiants

Citer

Matthieu Alfaro, François Hamel, Lionel Roques. Propagation or extinction in bistable equations: the non-monotone role of initial fragmentation. Discrete and Continuous Dynamical Systems - Series S, 2024, 17 (4), pp.1460-1484. ⟨10.3934/dcdss.2023165⟩. ⟨hal-04055502⟩
32 Consultations
45 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More