Boundary conditions for first-order hyperbolic relaxation systems

Organizers

Zhen Li , Xin Liang , Zhi Ting Ma , Hamid Mofidi , Li Wang , Fan Sheng Xiong , Shuo Yang , Wu Yue Yang

Speaker

Yizhou Zhou

Time

Thursday, March 27, 2025 3:00 PM - 4:00 PM

Venue

Online

Zoom 787 662 9899 (BIMSA)

Abstract

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.