Year: 2014
Type: article
Abstract: We consider a class of nonlocal reaction-diffusion problems, referred to as replicator-mutator equations in evolutionary genetics. By using explicit changes of unknown function, we show that they are equivalent to the heat equation and, therefore, compute their solution explicitly. Based on this, we then prove that, in the case of beneficial mutations in asexual populations, solutions dramatically depend on the tails of the initial data: they can be global, become extinct in finite time, or even be defined for no positive time. In the first case, we prove that solutions are accelerating, and in many cases converge for large times to some universal Gaussian profile. This sheds light on the biological relevance of such models.
DOI: 10.1137/140979411
Authors: Matthieu Alfaro, Rémi Carles
Language: English
Field: Medicine
Domain: Health Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
OpenAlex ID: W2053846060