报告题目：Perthame-Souganidis mutation-selection model and extensions
报告人：Prof. Yuan Lou (Ohio State University)
报告摘要：To study the evolution of conditional dispersal we extend the Perthame-Souganidis mutation-selection model and consider an integro-PDE model for a population structured by the spatial variables and one trait variable. We assume that both diffusion rate and advection rate are functions of the trait variable, which lies within a short interval I. Under proper conditions on the invasion fitness gradient, we show that in the limit of small mutation rate, the positive steady state will concentrate in the trait variable and forms a Dirac mass supported at one end of I，or a Dirac mass supported at the interior of I, or two Dirac masses supported at both ends of I. This is based on joint works with Wenrui Hao (Penn State) and King-Yeung Lam (Ohio State).
报告题目：A Free Boundary Problem for modeling Plaques in the Artery
报告人：Professor Bei Hu, University of Notre Dame
报告摘要：Atherosclerosis is a leading cause of death worldwide; it originates from a plaque which builds up in the artery. We considered a simplified model of plaque growth involving LDL and HDL cholesterols, macrophages and foam cells, which satisfy a coupled system of PDEs with a free boundary, the interface between the plaque and the blood flow. We proved that there exist small radially symmetric stationary plaques and established a sharp condition that ensures their stability. We also determined necessary and sufficient conditions under which a small initial plaque will shrink and disappear, or persist for all times.
邀请人： 陆国震 教授