Selection-mutation dynamics with asymmetrical reproduction kernels. (English) Zbl 1496.35398
This work mathematically studies some selection-mutation models of nonlocal type, describing the distribution of a sexual population structured by a phenotypical trait. The novelty consists in considering an asymmetry in the trait heredity or in the fecundity between the parents, situations that occur, for example, in certain mosquitoes species.
The main results are related to the asymptotic behavior of the population distribution. In particular, some non-extinction conditions and BV estimates on the total population are provided. Moreover, concentration phenomena are considered: some general estimates are given for the Hamilton-Jacobi equations that arise from this study, and concentration is obtained in some special situations.
The main results are related to the asymptotic behavior of the population distribution. In particular, some non-extinction conditions and BV estimates on the total population are provided. Moreover, concentration phenomena are considered: some general estimates are given for the Hamilton-Jacobi equations that arise from this study, and concentration is obtained in some special situations.
Reviewer: Andrea Tellini (Madrid)
MSC:
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 92D25 | Population dynamics (general) |
| 35F21 | Hamilton-Jacobi equations |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 45K05 | Integro-partial differential equations |
| 35R09 | Integro-partial differential equations |
| 35R07 | PDEs on time scales |
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