MATH6041 - Topics in Differential Equations I - 2020/21

General Information

Lecturer

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

Time and Venue

• Lecture: Tue 15:30-18:15 (Face-to-Face at AB1 G03, 20 Oct - 24 Nov)

Course Description

Topics in Differential Equations I - Some Topics in Hyperbolic Conservation Laws

Introduction to shock wave theory, Riemann Problems, Glimm Theory and Random choice methods, Uniqueness theory of viscosity solutions, stability of nonlinear waves, multi-dimensional hyperbolic conservation laws, non-uniqueness theory, Initial-boundary value problems, Formation of Singularities, Steady compressible flows.

Zoom Link (8 Sep - 13 Oct & 1 Dec):

https://cuhk.zoom.us/j/3869784315?pwd=V1Z0amxKaTJZci9ZQ1dPRXFVT3owZz09

Meeting ID: 386 978 4315

Passcode: (to be emailed to the students who take this course)

References

• J. A. Smoller: Shock Waves and Reaction-Diffusion Equations
• C. M. Dafermos: Hyperbolic Conservation Laws in Continuum Mechanics
• A. Majda: Compressible Fluid Flow and System of Conservation Laws in Several Space Variables
• D. Serre: Systems of Conservation Laws, Vols. 1 & 2, 1999

Lecture Notes

• An Overview of Shock Wave Theory
• Chapter 1
• Chapter 2
• Chapter 3

Quizzes and Exams

• Final Grades

Assessment Scheme

Honesty in Academic Work

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and thereby help avoid any practice that would not be acceptable.