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- W2045975047 abstract "We show that the solution to a nonlocal reaction–diffusion equation, present in evolutionary genetics, can be related explicitly to the solution of the heat equation with the same initial data. As a consequence, we show different possible scenario for the solution: it can be either well-defined for all time, or become extinct in finite time, or even be defined for no positive time. In the former case, we give the leading-order asymptotic behavior of the solution for large time, which is universal. Nous montrons que les solutions d'une équation de réaction–diffusion non locale, utilisée en génétique évolutive, peuvent être exprimées en fonction de la solution de l'équation de la chaleur avec même donnée initiale. Nous en déduisons plusieurs scénarios possibles pour la solution : elle peut, soit être définie pour tout temps, soit devenir identiquement nulle en temps fini, ou encore n'être définie pour aucun temps positif. Dans le premier cas, nous donnons le comportement asymptotique en temps grand de la solution, faisant intervenir un profil universel." @default.
- W2045975047 created "2016-06-24" @default.
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- W2045975047 date "2015-03-01" @default.
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- W2045975047 title "Explicit solutions in evolutionary genetics and applications" @default.
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- W2045975047 doi "https://doi.org/10.1016/j.crma.2014.11.018" @default.
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