A tutorial on hyperbolic conservation laws. Lecture 1

Monday, July 13, 2009 - 3:30pm - 4:45pm
EE/CS 3-180
Alberto Bressan (The Pennsylvania State University)
This set of lectures will provide a basic introduction to
hyperbolic systems of conservation laws in one space dimension.
The main topics covered will be:

  1. Meaning of the conservation equations and
    definition of weak solutions.

  2. Shocks, Rankine-Hugoniot equations and admissibility

  3. The Riemann problem. Wave interaction estimates.

  4. Weak solutions to the Cauchy problem with small BV data.

  5. Uniqueness and continuous dependence.

  6. Vanishing viscosity approximations.

  7. Some counter-examples to global existence,
    uniqueness, and continuous dependence of solutions,
    when some key hypotheses are removed.

MSC Code: