MATH6041 - Topics in Differential Equations I - 2021/22

Course Year: 
2021/22
Term: 
1

General Information

Lecturer

  • Professor Zhouping Xin
    • Office: AB1 701
    • Tel: 3943 4100
    • Email:

Time and Venue

  • Lecture: Tue 15:30-18:15, AB1 G03

Course Description

- Introductions of general theory of multi-dimensional Conservation Laws

- Uniqueness Theory of Viscosity Solutions for 1-D systems

- Local well-posedness of M-D systems (IVP & IBVP)

- Formation of singularities (Shock formation and shock development problem)

- Structural stability of elementary waves

- Theory of steady compressible flows

- Non-uniqueness and convex integrations

- Other current topics (if time is allowed, such as vacuum dynamics)


References

  • 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: Vol. 1&2, 1999
  • R. Courant and K. O. Froiedrichs, Supersonic Flow and Shock Waves, Interscience Publishers, Inc., New York, 1948
  • Lipman Bers, Mathematical Aspects of Subsonic and Transonic Gas Dynamics, Wiley, New York, 1958

Lecture Notes


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 28, 2021 16:26:40