Approximate solutions to hyperbolic systems of conservation laws may be generated in a variety of ways: by the method of vanishing viscosity, through difference approximations, by relaxation schemes, etc. As we have seen in earlier chapters, sequences of approximate solutions that are merely bounded in some Lp space generate in the limit measure-valued solutions that may exhibit high-frequency oscillations and/or concentrations. The aim is to demonstrate that the action of entropy inequalities may quench rapid oscillations, thus enforcing strong convergence of the approximating solutions to weak solutions of the systems. Some indication of this effect was alluded to in Section 1.7.