ABSTRACT
In this chapter, the authors consider the Cauchy problem for the scalar conservation law. The study of the single equation has a long history and the existence and uniqueness of the generalized solution for this equation has been well studied. As the simplest model of hyperbolic conservation laws, Tartar first introduced the theory of compensated compactness to the scalar equation and succeeded in obtaining a new method, called the compensated compactness method, to study the global existence of generalized solutions for hyperbolic conservation laws. The authors give a simple proof of existence of global generalized solutions to the Cauchy problem of scalar conservation law.
