Abstract: We consider a nonlocal, nonlinear equation describing the evolution of a population structured with a phenotypic trait. The dynamics governed by the adaptation to the environment depending on how fit the phenotypic trait is and the small mutations to reach the fittest traits in the long-time. Thus, in a regime of long-time and small mutations, the population concentrates on a set of dominant traits and this can be described by a constrained Hamilton-Jacobi equation mathematically. We propose an asymptotic preserving numerical scheme for this problem. We show that the scheme is convergent in all the regimes and it is stable in the long-time and small mutations limit. We prove that the limiting scheme converges to the viscosity solution of the Hamilton-Jacobi equation. The talk is based on a joint work with V. Calvez and H. Hivert (arXiv:2204.04146, 2022).
An asymptotic preserving scheme for a concentration phenomenon in a Lotka-Volterra type parabolic PDE
15.06.2022 15:15 - 16:00
Organiser:
SFB 65, DK
Location:
TU Wien (Gußhausstraße 25-27, 2. Stock, EI4 Reithoffer HS) und Zoom
Verwandte Dateien
- pde_afternoon_2022-06-15.pdf 498 KB