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Boundary conditions for first-order hyperbolic relaxation systems

组织者

李震 , 梁鑫 , 马志婷 , 哈米德·莫菲迪 , 王丽 , 熊繁升 , 杨朔 , 杨武岳

演讲者

周一舟

时间

2025年03月27日 15:00 至 16:00

地点

Online

线上

Zoom 787 662 9899 (BIMSA)

摘要

The first-order hyperbolic relaxation system is a class of time-dependent partial differential equations which model various non-equilibrium phenomena. For such systems, the main interest is to understand the zero relaxation limit. The initial-value problem for the relaxation system has been well-developed and a systematical framework has been built. However, the initial-boundary value problem of the relaxation system is still in the developing stage. In this talk, I will first introduce the theory of boundary conditions for general relaxation systems. Then I will present the recent results for the initial-boundary-value problem with characteristic boundaries. Specifically, we redefine a characteristic Generalized Kreiss condition (GKC) which is essentially necessary to have a well-behaved relaxation limit. Under this characteristic GKC and a Shizuta-Kawashima-like condition, we derive reduced boundary conditions for the relaxation limit solving the corresponding equilibrium systems and justify the validity.