ABSTRACT
In this chapter, the authors describe some work dealing with weak limits of solutions to non-linear systems of partial differential equations. They begin by discussing the general structure of the problem and then turn to the special setting of mechanics. The maximum separation occurs in the setting of elliptic systems for which the wave cone and constitutive manifold are separated by a hyperplane. In the absence of an entropy condition, the wave cone and constitutive manifold are not separated for a hyperbolic system of conservation laws. In treating approximation methods such as the viscosity method and finite difference schemes one encounters inhomogeneous systems.
