Shock Structures Described by Hyperbolic Balance Laws

In this paper we consider shock structures that arise in systems of hyperbolic balance laws, i.e. hyperbolic systems of conservation laws with source terms. We show how the Whitham criterion for the existence of such shock structures can be extended to systems with more than one relaxation variable. In addition, we develop a method that is useful for determining the stability of the equilibrium states of such systems. The utility of this method is illustrated by a number of examples.