MATH6041  Topics in Differential Equations I  2022/23
General Information
Lecturer

Zhouping XIN
 Office: AB1 701
 Tel: 3943 4100
 Email:
Time and Venue
 Lecture: Tue 16:3019:15, 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 multidimensional theory:
~ Nonuniqueness results;
~ Singularityformation;
~ Boundaryvalue problems.
References
 J. A. Smoller: Shock Waves and ReactionDiffusion Equations, SpringVerlag
 C. M. Dafermos: Hyperbolic Conservation Laws in Continuous Mechanics
 Alberto Bressan: Hyperbolic Systems of Conservation Laws: OneDimensional 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:
http://www.cuhk.edu.hk/policy/academichonesty/and thereby help avoid any practice that would not be acceptable.
Assessment Policy Last updated: September 07, 2022 16:05:11