Existence and Uniqueness of Entropy Solution of Scalar Conservation Laws with a Flux Function Involving Discontinuous Coefficients

ABSTRACT

In this paper, the question of existence and uniqueness for entropy solutions of scalar conservation laws with a flux function which is discontinuous with respect to the space variable is investigated. We show that no extra assumption of convexity or genuine non-linearity with respect to the state variable of the flux function is required for the problem to be well-posed and prove it. The proof uses a kinetic formulation of the conservation law.