Introduction to hyperbolic partial differential equations and conservation laws
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.
Lecturer
Tianwen Luo
Date
21st February ~ 20th June, 2023
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday | 09:50 - 12:15 | Tsinghua-Ningzhai-W11 | ZOOM 07 | 559 700 6085 | BIMSA |
Prerequisite
Multi-variable Calculus, Basic Partial Differential Equation, Basics of Riemannian Geometry(optional)
Syllabus
(Tentative) characteristics hypersurfaces, Riemann problem, Riemann invariant, shocks formation, rarefaction waves, elementary waves, entropy, compressible fluids, supersonic flows, domain of dependence, acoustical geometry
Reference
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
2. J. Smoller, Shock Waves and Reaction—Diffusion Equations
3. D. Christodoulou and S. Miao, Compressible flow and Euler’s equations
Audience
Graduate
Video Public
No
Notes Public
No
Language
Chinese