主持人: 何小清 青年研究员
报告平台: 腾讯会议 ID：112 240 158（https://meeting.tencent.com/s/daNQDcJvn3gk）
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.