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Effective boundary conditions of diffusion equations on domains containing thin layers
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报告题目:Effective boundary conditions of diffusion equations on domains containing thin layers
    报告人:  王学峰 教授  南方科技大学

邀请人:吴事良 教授
    报告时间:6月1日14:30-15:30
    报告地点:信远楼II206数统院报告厅

报告人简介:  王学锋,南方科技大学教授,博导,国家“千人计划”获得者。主要研究方向是偏微分方程及其应用。1984年、1986年先后于北京大学数学系获学士学位和硕士学位,1990年于美国明尼苏达大学数学学院获博士学位。先后在美国明尼苏达大学、美国犹他大学和香港浸会大学等做访问研究员或访问教授。主持美国国家科学基金项目多项,若干论文发表在《CPAM》、《Duke Math.J》、《ARMA》、《SIAM》、《TAMS》、《CMP》等国际重要数学杂志上,论文被他引总共1100多次,近三年来在国际学术会议上给了20多个特邀报告,现担任一些国际重要数学杂志的编委或副主编。

报告摘要:This is going to be a survey talk on a class of diffusion equations. 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. 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, as well as results that have not been published. These results not only are of practical significance, but also bring some new challenges to pure PDE-research.

 

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