双曲偏微分方程与守恒律简介

The course introduces hyperbolic partial differential equations and conservation laws from both historical and modern perspectives, focusing on important examples rather than general theory. The classical concepts such as characteristics and Riemann invariant plays an indispensable role in the recent development, including black holes in relativity and shocks in gas dynamics.

讲师

罗天文

日期

2023年02月21日至 06月20日

位置

Weekday	Time	Venue	Online	ID	Password
周二	09:50 - 12:15	Tsinghua-Ningzhai-W11	ZOOM 07	559 700 6085	BIMSA

修课要求

Multi-variable Calculus, Basic Partial Differential Equation, Basics of Riemannian Geometry(optional)

课程大纲

(Tentative) characteristics hypersurfaces, Riemann problem, Riemann invariant, shocks formation, rarefaction waves, elementary waves, entropy, compressible fluids, supersonic flows, domain of dependence, acoustical geometry

参考资料

1. R. Courant and K. O. Friedrichs, Supersonic flow and shock waves,
2. J. Smoller, Shock Waves and Reaction—Diffusion Equations
3. D. Christodoulou and S. Miao, Compressible flow and Euler’s equations

听众

Graduate

视频公开

不公开

笔记公开

不公开

语言

中文