Partially dissipative systems: hypocoercivity and hyperbolisation
数学专题报告
报告题目(Title)：Partially dissipative systems: hypocoercivity and hyperbolisation
报告人(Speaker)：Prof. Timothee Crin-Barat (Toulouse Mathematics Institute, France)
地点(Place)：Zoom ID: 838 903 07333 Password: 123456
时间(Time)：2025年11月3日（周一）16:00-17:00
邀请人(Inviter)：薛留堂
报告摘要
In this talk, we review recent results on so-called partially dissipative hyperbolic systems. Such systems model physical phenomena with degenerate dissipative terms and appear in many applications. For example, in gas dynamics where the mass is conserved during the evolution, but the momentum balance includes a diffusion (viscosity) or a damping (relaxation) term. First, using tools from the hypocoercivity theory and precise frequency decompositions, we derive sharp stability estimates for linear systems satisfying the Kalman rank condition. This linear analysis allows us to establish new global-in-time existence and large-time behaviour results in a critical regularity framework for nonlinear systems. Then, we interpret partially dissipative systems as hyperbolic approximations of parabolic systems, in the context of the paradox of heat conduction. In particular, we focus on a hyperbolic approximation of the compressible Navier-Stokes-Fourier system and establish its hyperbolic-parabolic strong relaxation limit.
