On the uniqueness of solution to generalized chaplygin gas

Abstract

The main object of the paper is finding a unique solution to Riemann problem for generalized Chaplygin gas model. That is a model of the dark energy in Universe introduced in the last decade. It permits an infinite mass concentration so one has to consider solutions containing the Dirac delta function. Although it was easy to construct solution to any Riemann problem, the usual admissibility conditions, overcompressiveness, do not exclude unwanted delta-type waves when a classical solution exists. We are using Shadow Wave approach in order to solve that uniqueness problem since they are well adopted for using Lax entropy–entropy flux conditions and there is a rich family of convex entropies.