MATH6041 - Topics in Differential Equations I - 2021/22

Course Year: 

General Information


  • 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)


  • 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%

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Assessment Policy

Last updated: November 24, 2021 14:20:06