Abstract:

In this talk, I will introduce our 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.

主讲人简介：雍稳安，1992年于德国海德堡大学取得博士学位，2005年于海德堡大学取得德国教授资格（Habilitation），同年加盟清华大学，现为清华大学数学科学系长聘教授。研究兴趣包括应用偏微分方程、数值方法、非平衡态热力学、数学建模以及机器学习。主要学术贡献有：系统地创立了双曲松弛偏微分方程的数学理论、建立了格子Boltzmann方法的稳定收敛性理论、提出了正确描述可压缩粘弹性流体流动的数学模型、提出了非平衡态热力学的守恒耗散理论（CDF）等。是英国介观过程科学联盟（UKCOMES）的国际学术顾问，其在控制方面的工作曾被国际科技媒体Advances in Engineering遴选报道。