# An introduction to multidimensional conservation laws. Lecture 1

Monday, July 13, 2009 - 10:45am - 11:45am

EE/CS 3-180

Gui-Qiang Chen (Northwestern University)

This series of four lectures will provide an introduction

to multidimensional conservation laws, along with a perspective on a

list of open problems. The main topics will include:

to multidimensional conservation laws, along with a perspective on a

list of open problems. The main topics will include:

- Prototypes and Basic Features/Phenomena
- Multidimensional Models
- Multidimensional Steady Problems
- Multidimensional Self-Similar Problems
- Compressible Vortex Sheets and Related Problems
- Divergence-Measure Fields and Hyperbolic Conservation

Laws

Lecture References:

- Gui-Qiang Chen, Euler Equations and Related Hyperbolic

Conservation Laws, In: Handbook of Differential Equations:

Evolutionary Differential Equations, Vol. 2, pp. 1-104, 2005,

Eds. C.~M. Dafermos and E. Feireisl, Elsevier: Amsterdam,

Netherlands - Gui-Qiang Chen and Mikhail Feldman,

Shock Reflection-Diffraction and Multidimensional

Conservation Laws, In: Proceedings of the 2008 Hyperbolic

Conference: Theory, Numerics, and Application, AMS: Providence,

2009. - Gui-Qiang Chen, Monica Torres, and William Ziemer,

Measure-Theoretical Analysis and Nonlinear Conservation Laws,

Pure Appl. Math. Quarterly, 3 (2007), 841-879

(To Leon Simon on his 60th birthday). - Gui-Qiang Chen, Marshall Slemrod, and Dehua Wang,

Conservation

Laws: Transonic Flow and Differential Geometry, In: Proceedings

of

the 2008 Hyperbolic Conference: Theory, Numerics, and

Application,

AMS: Providence, 2009.

*You may directly download them from

http://www.math.northwestern.edu/~gqchen/preprints/

MSC Code:

35L65

Keywords: