I plan to cover the following topics: Euler equations; Burger's equation; p-system; symmetric hyperbolic PDE's; shock formation; Lax method of solving Riemann problems; Glimm's method for solving Cauchy problems; Entropy solutions; artificial viscosity.
Bibliography
- Joel Smoller, Shock waves and Reaction Diffusion Equations
- Constantine Dafermos, Hyperbolic Conservation Laws in Continuum Physics
- Alexandre Chorin and Jerrold Marsden, A Mathematical Introduction to Fluid Mechanics
- Lecture notes of Blake Temple (on his webpage)