ABSTRACT
This chapter focuses on the applications on hyperbolic conservation systems of two equations. It explains that the types are distinguished by hyper-bolicity, linearity and so on. The applications of the compensated compactness method on conservation laws depend strongly on the constructions of entropies of hyperbolic systems we considered. This is why, until now, almost all the results obtained by this method are only for systems of two equations. Similar to the scalar equation, for a given hyperbolic system, people first need to construct its approximation solutions, for instance, the sequence of viscosity solutions given by the Cauchy problem.
