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 15:3018:15, AB1 G03
Course Description
 Introductions of general theory of multidimensional Conservation Laws
 Uniqueness Theory of Viscosity Solutions for 1D systems
 Local wellposedness of MD systems (IVP & IBVP)
 Formation of singularities (Shock formation and shock development problem)
 Structural stability of elementary waves
 Theory of steady compressible flows
 Nonuniqueness and convex integrations
 Other current topics (if time is allowed, such as vacuum dynamics)
References
 J. A. Smoller: Shock Waves and ReactionDiffusion Equations, SpringVerlag
 C. M. Dafermos: Hyperbolic Conservation Laws in Continuous Mechanics
 Alberto Bressan: Hyperbolic Systems of Conservation Laws: OneDimensional 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
Assessment Scheme
Each student will be asked to report on a topic assigned by the teacher (the topic can be a paper related to the course or report on the content learned in the class).  100% 
Honesty in Academic Work
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http://www.cuhk.edu.hk/policy/academichonesty/and thereby help avoid any practice that would not be acceptable.
Assessment Policy Last updated: November 24, 2021 14:20:06