MATH6041A - Topics in Differential Equations I - 2023/24

Course Year: 


  • Course outline [Download file]
  • Class on 17 Oct 2023 - SUSPENDED
  • Class on 31 Oct 2023 - encouraged to attend the conference:
  • Two make-up classes will be scheduled

General Information


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

Time and Venue

  • Lecture: Tue 15:30-18:15, AB1 G03

Course Description

Some topics on Multi-Dimensional Systems of Hyperbolic Conservation Laws:

(i) Introduction;

(ii) Cauchy problem and Friedrich’s theory on Symmetric hyperbolic systems;

(iii) Blow-up of Smooth Solutions and formation of shocks:

-- Scalar equations;

-- Plane waves and formation of shocks for 1D systems;

-- Sideris theory of blow-up of smooth solutions to the compressible Euler systems.

(iv) IBVP;

(v) Weak solutions:

-- Shock front solutions;

-- Rarefaction waves;

-- Contact discontinuities;

-- Some physical wave patterns;

-- Transonic flows

-- Non-uniqueness of weak solutions.

(vi) Other related topics……


  • Tai Ping Liu, Shock Waves, 215 AMS
  • J. A. Smoller: Shock Waves and Reaction-Diffusion Equations, Spring-Verlag
  • C. M. Dafermos: Hyperbolic Conservation Laws in Continuous Mechanics
  • A. Majda: Compressible Fluid Flows and System of Conservation Laws in Several Space Variables
  • D. Serre: Systems of Conservation Laws: Vol. 1 & 2, 1999

Lecture Notes

Assessment Scheme

Each student will be asked to write a report on a topic assigned by the teacher. 100%

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Assessment Policy

Last updated: November 22, 2023 12:34:07