报告题目：Dynamics of Two Structured Population Models

报告时间：2022-01-06  15:00 - 16:00

报告人：阮欣然 助理教授 首都师范大学

腾讯会议ID：345 773 4983 会议密码：174675

Abstract：Structured population models offer us a powerful way of studying the adaptive dynamics of some hidden characteristic, or “trait”, which varies from individual to individual. In this talk, I will introduce two models we recently studied, namely the age-structured model and the space-structured cell growth model with heterogeneous mobility. In the age-structured population model without mutation, the solution will converge to Dirac functions in the phenotypical direction, which makes the numerical simulation of the model challenging. In the talk, I will briefly review some asymptotic results of the model and further introduce an asymptotic preserving (A-P) scheme based on the WKB ansatz of the solutions. With the method, we can accurately capture the concentrations on a coarse, parameter-independent mesh. Important properties, including the A-P property, are rigorously proved. Its generalization to the case with mutation will be introduced as well. In the space-structured cell growth model with heterogeneous mobility, it is normal to assume that the more mobile cells are less proliferative and vice versa. Via an implicit finite difference scheme specifically designed for the model, we find that, in the case where mobility is bounded, a traveling front emerge, while in the case where mobility is unbounded, a stretching front may appear. Formal asymptotic analysis of the limit solution will be presented. In particular, we will explain why there is no traveling front with an unbounded mobility.