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科学研究
RESEARCH
Effective boundary conditions of diffusion equations on domains containing thin layers
时间  Datetime
2020-11-20 16:00 — 17:00
地点  Venue
Zoom APP(2)()
报告人  Speaker
Xuefeng Wang
单位  Affiliation
Chinese University of Hong Kong, Shenzhen
邀请人  Host
谢春景
备注  remarks
Zoom ID: 695 952 01432; Password: 749849
报告摘要  Abstract

In this survey talk, of concern is the following scenario: a domain consists of two parts, with one of them being a thin layer; on the domain we have a diffusion equation, one of whose physical parameters such as diffusion coefficient has different size scales on different subdomains. This kind of problem arises in real applications such as thermal barrier coatings of turbine engine blades, and effects of roads on the spreading of populations and epidemics, cell membranes. Numerical computation of such a diffusion equation on such a domain is time-consuming because we would need very fine grids on the thin layer; moreover, we cannot see easily the effects of the thin layer on the dynamics of the diffusion equation. A good way to resolve this problem is to think of the thin layer as a thickless surface/curve, on which we impose an effective boundary condition (EBC); then hopefully with ease we can solve, numerically, the diffusion equation on the remaining subdomain with the EBC; furthermore, we can see the effects of the thin layer via EBC. We will review classic theorems, and introduce results obtained in recent years. These results not only are of practical significance, but also bring some new challenges to pure PDE-research.