Kinetic formulation and uniqueness for scalar conservation laws with   discontinuous flux
  We prove a uniqueness result for BV solutions of scalar conservation laws with discontinuous flux in several space dimensions. The proof is based on the notion of kinetic solution and on a careful analysis of the entropy dissipation along the discontinuities of the flux. 
Graziano Crasta, Virginia De Cicco, Guido De Philippis
math.AP