Partially dissipative hyperbolic systems:
hypocoercivity and hyperbolic
approximations
报告专家：Timothée Crin-Barat博士（Université Toulouse III-Paul Sabatier, France）
报告时间：7月11日（星期五）下午4:00-5:00
报告地点：数学学院西303
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 behavior 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.
邀请人：张旭
