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