Title: Systems of Conservation Laws in Two Dimensions    
 
Abstract: Multi-dimensional systems of conservation
laws have been a major research target for many decades
and substantial progress has been made in recent years.
The National Science Foundation in the USA has been
supporting the research strongly and there are
many senior experts in China in this area.
We expect that there will be great progress in the
near future. We plan to introduce the topic at an entry
level and bring the participants to the research height.
The primary system is the Euler system for ideal 
compressible gases. There are several simplified models 
which are the 2-D unsteady transonic small 
disturbance system, potential flows, isentropic system, 
and the pressure gradient system. The issues are 
existence, uniqueness, and structures of solutions to 
various initial and boundary value problems.
Our focus will be on special initial data that yield
solutions with distinctive physical characteristics.
These types of initial data are collectively called
Riemann data and the corresponding solutions are 
self-similar in space-time. Typical types of physical 
features are regular and Mach reflections. Thus we 
will cover Riemann problems in two space dimensions
and explain features of shock reflections. The 
mathematical tools include theory of characteristics, 
elliptic estimates, boundary corner regularity, fixed 
point theorems, numerical simulations, and asymptotic 
analysis. 

Prerequisite:
It is desirable that the participants have taken a 
one-semester course on the basic 1-d Riemann problems 
for hyperbolic and genuinely nonlinear systems.
A reference book is L. C. Evans: Partial Differential
equations. Another is Y. Zheng: Systems of Conservation
Laws, Two-dimensional Riemann Problems (Part I).  

Text: No textbook available. The materials will be from
research journals.