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 16:30-19:15, 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 multi-dimensional theory:

~ Non-uniqueness results;

~ Singularity-formation;

~ Boundary-value problems.

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: Vols 1 & 2, 1999.

Assessment Scheme

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