A Hamilton-Jacobi Approach to Evolution of Dispersal - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Communications in Partial Differential Equations Year : 2022

A Hamilton-Jacobi Approach to Evolution of Dispersal


The evolution of dispersal is a classical question in evolutionary biology, and it has been studied in a wide range of mathematical models. A selection-mutation model, in which the population is structured by space and a phenotypic trait, with the trait acting directly on the dispersal (diffusion) rate, was formulated by Perthame and Souganidis [Math. Model. Nat. Phenom. 11 (2016), 154-166] to study the evolution of random dispersal towards the evolutionarily stable strategy. For the rare mutation limit, it was shown that the equilibrium population concentrates on a single trait associated to the smallest dispersal rate. In this paper, we consider the corresponding evolution equation and characterize the asymptotic behaviors of the time-dependent solutions in the rare mutation limit, under mild convexity assumptions on the underlying Hamiltonian function.
Fichier principal
Vignette du fichier
Evolution_Trait_Dispersal_Final.pdf (466.24 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03835868 , version 1 (01-11-2022)


  • HAL Id : hal-03835868 , version 1


King-Yeung Lam, Yuan Lou, Benoît Perthame. A Hamilton-Jacobi Approach to Evolution of Dispersal. Communications in Partial Differential Equations, In press. ⟨hal-03835868⟩
31 View
25 Download


Gmail Facebook Twitter LinkedIn More