Convergence of a discrete selection-mutation model with exponentially decaying mutation kernel to a Hamilton-Jacobi equation
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914243652091904 |
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| author | Jeddi, Anouar |
| author_facet | Jeddi, Anouar |
| contents | In this paper we derive a constrained Hamilton-Jacobi equation with obstacle from a discrete non-linear integro-differential model of population dynamics, with exponentially decaying mutation kernel. The exponential decay of the kernel leads to a modification of the classical Hamilton-Jacobi equation obtained previously from continuous models in \cite{BMP}. We consider a population composed of individuals characterized by a quantitative trait, subject to selection, mutation and competition. In a regime of small mutations, small spatial discretization step and large time we prove that the WKB transformation of the density converges to a viscosity solution of a constrained Hamilton-Jacobi equation with obstacle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_06657 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence of a discrete selection-mutation model with exponentially decaying mutation kernel to a Hamilton-Jacobi equation Jeddi, Anouar Analysis of PDEs In this paper we derive a constrained Hamilton-Jacobi equation with obstacle from a discrete non-linear integro-differential model of population dynamics, with exponentially decaying mutation kernel. The exponential decay of the kernel leads to a modification of the classical Hamilton-Jacobi equation obtained previously from continuous models in \cite{BMP}. We consider a population composed of individuals characterized by a quantitative trait, subject to selection, mutation and competition. In a regime of small mutations, small spatial discretization step and large time we prove that the WKB transformation of the density converges to a viscosity solution of a constrained Hamilton-Jacobi equation with obstacle. |
| title | Convergence of a discrete selection-mutation model with exponentially decaying mutation kernel to a Hamilton-Jacobi equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2412.06657 |