Concentration in Lotka-Volterra parabolic or integral equations: a general convergence result - Laboratoire Jacques-Louis Lions Accéder directement au contenu
Article Dans Une Revue Methods and Applications of Analysis Année : 2009

Concentration in Lotka-Volterra parabolic or integral equations: a general convergence result

Sepideh Mirrahimi
Benoît Perthame

Résumé

We study two equations of Lotka-Volterra type that describe the Darwinian evolution of a population density. In the first model a Laplace term represents the mutations. In the second one we model the mutations by an integral kernel. In both cases, we use a nonlinear birth-death term that corresponds to the competition between the traits leading to selection. In the limit of rare or small mutations, we prove that the solution converges to a sum of moving Dirac masses. This limit is described by a constrained Hamilton-Jacobi equation. This was already proved by B. Perthame and G. Barles for the case with a Laplace term. Here we generalize the assumptions on the initial data and prove the same result for the integro-differential equation.
Fichier principal
Vignette du fichier
BMP_2.pdf (208.64 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00371416 , version 1 (27-03-2009)
hal-00371416 , version 2 (20-09-2017)

Identifiants

Citer

Guy Barles, Sepideh Mirrahimi, Benoît Perthame. Concentration in Lotka-Volterra parabolic or integral equations: a general convergence result. Methods and Applications of Analysis, 2009, 16 (3), pp.321-340. ⟨10.4310/MAA.2009.v16.n3.a4⟩. ⟨hal-00371416v2⟩
318 Consultations
235 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More