ON EXISTENCE AND UNIQUENESS OF ENTROPY SOLUTIONS TO THE CAUCHY PROBLEM FOR A CONSERVATION LAW WITH DISCONTINUOUS FLUX

摘要

We study the Cauchy problem for a conservation law with space discontinuous flux of generalized Audusse-Perthame form. It is shown that, after a change of unknown function, entropy solutions in the sense of Audusse-Perthame correspond to Kruzhkov's generalized entropy solutions for the transformed equation. This observation allows to use the Kruzhkov method of doubling variable ( instead of rather complicated variant of this method invented by Audusse and Perthame). Applying this method for measure-valued solutions, we establish the uniqueness and the existence of entropy solutions to the problem under consideration.