COSTA, Manon; ETCHEGARAY, Christèle; MIRRAHIMI, Sepideh

doi:10.1016/j.nonrwa.2020.103239

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COSTA, Manon
Institut de Mathématiques de Toulouse UMR5219 [IMT]

ETCHEGARAY, Christèle
Modélisation Mathématique pour l'Oncologie [MONC]

MIRRAHIMI, Sepideh
Institut de Mathématiques de Toulouse UMR5219 [IMT]

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Nonlinear Analysis: Real World Applications. 2020, vol. 59

Elsevier

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2020

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We study a parabolic Lotka-Volterra type equation that describes the evolution of a population structured by a phenotypic trait, under the effects of mutations and competition for resources modelled by a nonlocal feedback. The limit of small mutations is characterized by a Hamilton-Jacobi equation with constraint that describes the concentration of the population on some traits. This result was already established in [BP08, BMP09, LMP11] in a time-homogenous environment, when the asymptotic persistence of the population was ensured by assumptions on either the growth rate or the initial data. Here, we relax these assumptions to extend the study to situations where the population may go extinct at the limit. For that purpose, we provide conditions on the initial data for the asymptotic fate of the population. Finally, we show how this study for a time-homogenous environment allows to consider temporally piecewise constant environments< Leer menos

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Parabolic integro-differential equations

Hamilton-Jacobi equation with constraint

Dirac concentrations

Adaptive evolution

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Survival criterion for a population subject to selection and mutations ; Application to temporally piecewise constant environments

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