MATH6041 - Topics in Differential Equations I - 2022/23

Course Year: 

General Information


  • Zhouping XIN
    • Office: AB1 701
    • Tel: 3943 4100
    • Email:

Time and Venue

  • Lecture: Tue 16:30-19:15, AB1 G03

Course Description

Course Contents:

- Introduction to shock wave theory, I (General)

- Introduction through the Burgers Equation, II

- Theory for general scalar conservation laws (Krushkov theory and compensated compactness)

- Shock formation problem

- Riemann Problems (Lax Theory)

- Glimm Theory and Random Choice method

- Front tracking method and Continuous dependence

- Uniqueness of viscosity solutions

- Large time asymptotic behavior of solutions

- Selected topics in multi-dimensional theory:

~ Non-uniqueness results;

~ Singularity-formation;

~ Boundary-value problems.


  • J. A. Smoller: Shock Waves and Reaction-Diffusion Equations, Spring-Verlag
  • C. M. Dafermos: Hyperbolic Conservation Laws in Continuous Mechanics
  • Alberto Bressan: Hyperbolic Systems of Conservation Laws: One-Dimensional Cauchy Problem
  • A. Majda: Compressible Fluid Flow and System of Conservation Laws in Several Space Variables
  • D. Serre: Systems of Conservation Laws: Vols 1 & 2, 1999.

Assessment Scheme

Each student will be asked to report on a topic assigned by the teacher (the topic can be a paper related to the course or report on the content learned in the class). 100%

Honesty in Academic Work

The Chinese University of Hong Kong places very high importance on honesty in academic work submitted by students, and adopts a policy of zero tolerance on cheating and plagiarism. Any related offence will lead to disciplinary action including termination of studies at the University. Although cases of cheating or plagiarism are rare at the University, everyone should make himself / herself familiar with the content of the following website:

and thereby help avoid any practice that would not be acceptable.

Assessment Policy

Last updated: September 07, 2022 16:05:11