Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Confining integro-differential equations originating from evolutionary biology: ground states and long time dynamics

Abstract : We consider nonlinear mutation selection models, known as replicator-mutator equations in evolutionary biology. They involve a nonlocal mutation kernel and a confining fitness potential. We prove that the long time behaviour of the Cauchy problem is determined by the principal eigenelement of the underlying linear operator. The novelties compared to the literature on these models are about the case of symmetric mutations: we propose a new milder sufficient condition for the existence of a principal eigenfunction, and we provide what is to our knowledge the first quantification of the spectral gap. We also recover existing results in the non-symmetric case, through a new approach.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-03376957
Contributor : Pierre Gabriel Connect in order to contact the contributor
Submitted on : Wednesday, October 13, 2021 - 7:06:36 PM
Last modification on : Wednesday, October 20, 2021 - 12:24:16 AM

Files

0-ground-state.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-03376957, version 1
  • ARXIV : 2110.07214

Collections

Citation

Matthieu Alfaro, Pierre Gabriel, Otared Kavian. Confining integro-differential equations originating from evolutionary biology: ground states and long time dynamics. 2021. ⟨hal-03376957⟩

Share

Metrics

Record views

23

Files downloads

20