CLICK HERE for the hand-written lecture notes of a mini-course on Hyperbolic Conservation Laws, I gave at the Summer School on Mathematical Methods of Statistical Physics, held in Prague, in September 1999. Thanks are due to Roman Kotecky for organising this wonderful series of events.
CONTENTS
Definitions, motivation, basic examples
Hyperbolicity
Characteristics, Riemann invariants
Weak solutions, jump discontinuities (shocks)
Rankine-Hugoniot conditions (for the spead of propagation of shocks)
Lax's stbility conditios: shocks
Rarefaction waves
Riemann's problem
Entropies
Entropy solutions
Existence of convex entropies: Lax's entropy waves, other computations
Vanishing viscosity, convergence: compensated compactness, Di Perna's program