ABSTRACT
In this chapter, we study certain properties which ensure that the Cauchy problem for a first order system of conservation laws is well posed. We begin with the study of weak solutions, satisfying the system of conservation laws in the distributional sense, and then outline the admissibility conditions which ensure uniqueness of solutions. Notions of simple waves and Riemann invariants are introduced, and some general properties of shocks and rarefaction waves are noted. The Riemann problem for shallow water equations is presented with some general remarks given at the end.
