Survival criterion for a population subject to selection and mutations ; Application to temporally piecewise constant environments
| hal.structure.identifier | Institut de Mathématiques de Toulouse UMR5219 [IMT] | |
| dc.contributor.author | COSTA, Manon | |
| hal.structure.identifier | Modélisation Mathématique pour l'Oncologie [MONC] | |
| dc.contributor.author | ETCHEGARAY, Christèle | |
| hal.structure.identifier | Institut de Mathématiques de Toulouse UMR5219 [IMT] | |
| dc.contributor.author | MIRRAHIMI, Sepideh | |
| dc.date | 2020 | |
| dc.date.accessioned | 2024-04-04T02:48:45Z | |
| dc.date.available | 2024-04-04T02:48:45Z | |
| dc.date.issued | 2020 | |
| dc.identifier.issn | 1468-1218 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191770 | |
| dc.description.abstractEn | 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 | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.subject.en | Parabolic integro-differential equations | |
| dc.subject.en | Hamilton-Jacobi equation with constraint | |
| dc.subject.en | Dirac concentrations | |
| dc.subject.en | Adaptive evolution | |
| dc.title.en | Survival criterion for a population subject to selection and mutations ; Application to temporally piecewise constant environments | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1016/j.nonrwa.2020.103239 | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| bordeaux.journal | Nonlinear Analysis: Real World Applications | |
| bordeaux.volume | 59 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-02126707 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02126707v1 | |
| bordeaux.COinS | ctx_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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