MATH6041A - Topics in Differential Equations I - 2023/24

Announcement

• Course outline [Download file]
• Class on 17 Oct 2023 - SUSPENDED
• Class on 31 Oct 2023 - encouraged to attend the conference: http://www.ims.cuhk.edu.hk/activities/conferences/30oct3nov2023/
• Two make-up classes will be scheduled

General Information

Lecturer

• 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……

References

• 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

• Pages 1-691

Assessment Scheme

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