偏微分方程系列报告

报告题目: Recent advances on boundary conditions for hyperbolic PDEs with relaxation

报告人:   雍稳安 教授 （清华大学）

报告摘要：

In this talk, I will introduce recent results about boundary conditions (BCs) for hyperbolic systems of partial differential equations with relaxation. Taking a linearized moment closure system as an example, we show that the structural stability of the system with conventionally proper BCs do not automatically guarantee a well-behaved zero relaxation limit. Motivated by this, we introduced a strengthened version of the classical Kreiss condition (called Generalized Kreiss condition) as a new criterion to examine the given BCs. Under the Generalized Kreiss condition, we derive reduced BCs for the limiting systems of the relaxation systems. For linearized problems, the validity of the reduced BCs can be verified rigorously. Furthermore, we show how the theory developed thus far can be used to construct proper BCs for the equations modeling non-equilibrium phenomena in spatial domains with boundaries.

报告人简介： 雍稳安，清华大学数学科学系教授，博士生导师，博士毕业于德国海德堡大学，随后在苏黎世联邦理工学院做博士后，在海德堡大学获德国教授资格。雍稳安教授主要研究带有松弛的一阶偏微分方程组，对这种类型的方程组建立了系统的数学理论，创立了非平衡态热力学的守恒耗散理论（CDF），提出迄今唯一正确描述可压缩粘弹性流体流动的数学方程，建立了格子波尔茨曼方法（LBM）的稳定性。相关论文发表在ARMA，C. PDE, SIAM系列，JDE等国际一流杂志。

报告时间: 2023.5.22(周一) 下午 4:00-5:30

报告地点: 逸夫楼1537