Scalar conservation law with discontinuous flux in a bounded domain

We consider the Dirichlet problem for a first-order hyperbolic equation with a convection term discontinuous with respect to the space variable. We introduce a definition of a weak entropy solution to the corresponding problem and then we prove existence and uniqueness of the entropy solution for a class of flux functions. The existence property is obtained by regularization of the flux function while for the uniqueness result we use the method of doubling variables and a Rankine-Hugoniot condition along the line of discontinuity.