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

hal.structure.identifierInstitut de Mathématiques de Toulouse UMR5219 [IMT]
dc.contributor.authorCOSTA, Manon
hal.structure.identifierModélisation Mathématique pour l'Oncologie [MONC]
dc.contributor.authorETCHEGARAY, Christèle
hal.structure.identifierInstitut de Mathématiques de Toulouse UMR5219 [IMT]
dc.contributor.authorMIRRAHIMI, Sepideh
dc.date2020
dc.date.accessioned2024-04-04T02:48:45Z
dc.date.available2024-04-04T02:48:45Z
dc.date.issued2020
dc.identifier.issn1468-1218
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191770
dc.description.abstractEnWe 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
dc.language.isoen
dc.publisherElsevier
dc.subject.enParabolic integro-differential equations
dc.subject.enHamilton-Jacobi equation with constraint
dc.subject.enDirac concentrations
dc.subject.enAdaptive evolution
dc.title.enSurvival criterion for a population subject to selection and mutations ; Application to temporally piecewise constant environments
dc.typeArticle de revue
dc.identifier.doi10.1016/j.nonrwa.2020.103239
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
bordeaux.journalNonlinear Analysis: Real World Applications
bordeaux.volume59
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-02126707
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02126707v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Nonlinear%20Analysis:%20Real%20World%20Applications&rft.date=2020&rft.volume=59&rft.eissn=1468-1218&rft.issn=1468-1218&rft.au=COSTA,%20Manon&ETCHEGARAY,%20Christ%C3%A8le&MIRRAHIMI,%20Sepideh&rft.genre=article


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