MATH6041 - Topics in Differential Equations I - 2021/22

General Information

Lecturer

• 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)

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: 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

• Section 1
• Section 2
• Section 3
• Section 4
• Section 5
• Section 6
• Section 7
• Section 8.1-8.4.3

Assessment Scheme

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