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曹锡华数学论坛 -方程分论坛
Some PDEs in Darwinian Dynamics
King-Yeung Lam 副教授(俄亥俄州立大学)
2021年1月15日上午8:30-9:30  腾讯会议

主持人: 何小清 青年研究员
报告时间: 2021年1月15日上午8:30-9:30
报告平台: 腾讯会议 ID:112 240 158(https://meeting.tencent.com/s/daNQDcJvn3gk)
主办单位:数学科学学院、科技处

报告人介绍:King-Yeung Lam, 美国俄亥俄州立大学副教授。2011年于美国明尼苏达大学获得博士学位,师从倪维明教授。在美国俄亥俄州立大学(OSU)先后为Mathematical Biosciences Institute 博士后、Zassenhaus助理教授、教授等。研究领域包含偏微分方程特别是抛物椭圆方程(组)和自由边界问题,及其在生物种群中的应用。已在“SIAM J. Appl. Math.”、“SIAM J. Math. Anal.”、“J. Differential Equations”、“Calc. Var. Partial Differential Equations”、“J. Funct. Anal.”、“Mem. Amer. Math. Soc.”、“Indiana Univ. Math. J.” “J. Math. Biol.”、“Bull. Math. Biol.”等国际著名SCI杂志上发表学术论文30多篇。

报告内容摘要:The evolution of dispersal is a classical question in evolutionary ecology, which has been widely studied with several mathematical models. The main question is to define the fittest dispersal rate for a population in a bounded domain, and, more recently, for traveling waves in the full space. In 2015, Perthame and Souganidis introduced a novel approach to study the evolution of unconditional dispersal. They considered an integro-PDE model for a population structured by the spatial variables and a (continuous) trait variable which is the random diffusion rate, and showed that, in the limit of vanishing mutations, the population concentrates on a single trait associated to the lowest dispersal rate. The mathematical interest stems from the asymptotic analysis which requires a completely different treatment of the different variables. For the space variable, the ellipticity leads to regularity results. For the trait variable, the concentration to a Dirac mass requires a different treatment. In our talk, we will talk about some recent developments, and the mathematical approach based on the WKB method and viscosity solutions leading to a constrained Hamilton-Jacobi equation.