Diffusion phenomena to partial differential equations from fluid dynamics

活动时间:2022-08-02 08:30-10:30、2022-08-05 08:30-10:30、2022-08-08 08:30-10:30、2022-08-11 08:30-10:30

活动地点:腾讯会议 465-9836-9400 



梅茗教授,1996年理学博士毕业于日本国立金泽大学,曾在日本的金泽大学担任讲师,并为日本文部省JSPS研究员。后在奥地利维也纳理工大学及加拿大的Alberta大学和McGill大学从事过博士后研究。梅茗教授研究方向为偏微分方程,主要从事流体力学中偏微分方程和生物数学中带时滞反应扩散方程研究,在偏微分方程领域中一流的数学杂志Archive Rational Math. Mech., SIAM J. Math. Anal., J. Differential Equations, Commun.PDEs 等学术刊物上公开发表论文100多篇,其中4篇论文为ESI高被引论文,并被《美国数学评论》评为SIAM J. Math.Anal.及J. Differential Equations的top author。


Compressible flow through porous media with a dissipative external force field is usually described as a p-system of hyperbolic conservation laws with damping, a kind of Euler equations. The damping effect makes the system behave as a set of nonlinear diffusion equations, and the solutions possessing diffusion characters are known as nonlinear diffusion waves. Similar phenomena also occur in the hydrodynamic system for the models of semiconductor devices (Euler-Poisson equations). In this short course, we systematically introduce such kind systems of equations, and show how these equations behave like the corresponding nonlinear diffusion equations. The historical background and the new development, as well as the open questions, all will be addressed. 

This course is designed for graduates and young researchers with background in partial different equations. The main aim is to introduce the basic theory in the topic of nonlinear diffusions to PDES in fluid dynamics, as well as the frontier research progress, and to enhance the research interest for the graduates and young researchers and to encourage them to involve in.