报告题目：Asymptotic Analysis for Time-dependent PDE Models with Small Holes and Applications

主 讲 人：王海兵

单 位：东南大学

时 间：8月16日14:00

腾 讯 ID：815 574 002

摘 要：

In this talk, weconsider twotime-dependent PDE modelswith a cluster of small holes. Based on the time-domain boundary integral equation method, we derive the asymptotic expansion of the solution as the size of the holes goes to zero. Under certain geometrical constraints on the size and the minimum distance of the holes, we show that the solution is approximated by a linear combination of point-sources where the weights are given by the capacitance of each hole. A rigorous justification of the asymptotic expansion is shown under natural conditions on the cluster of holes. As an application of the asymptotic expansion, we derive, in the limit case when the holes are densely distributed and occupy a bounded domain, the equivalent effective medium that generates, approximately, the same solution as the cluster of holes. Finally, we numerically verify the asymptotic expansions by comparing the asymptotic approximations with the numerical solutions via the finite element method.

简 介：

王海兵，东南大学数学学院教授，博士研究生导师，主要从事数学物理反问题的研究。现任中国数学会计算数学分会常务委员。2012年获得北海道大学和东南大学的理学博士学位，2014年获得江苏省优秀博士学位论文，2016年入选江苏高校“青蓝工程”中青年学术带头人培养对象，2018年获得江苏省工业与应用数学学会第二届“工业与应用数学奖青年奖”，2020年获得江苏省数学会第七届江苏省“数学成就奖”。已作为负责人获得三项国家自然科学基金和一项江苏省自然科学基金，在SIAM系列刊物、IP、JCP、JDE等刊物上发表学术论文三十余篇。