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Journal Articles Communications in Partial Differential Equations Year : 2022

A Hamilton-Jacobi Approach to Evolution of Dispersal

Abstract

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.
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Dates and versions

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

Identifiers

  • HAL Id : hal-03835868 , version 1

Cite

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