ANALYSIS OF A SCALAR CONSERVATION LAW WITH A FLUX FUNCTION WITH DISCONTINUOUS COEFFICIENTS

We study here a model of a conservation law with a flux function with discontinuous coefficients, namely the equation u(t)+(k(x)g(u)+ f (u))(x) = 0. We prove the existence and the uniqueness of an entropy solution in L-infinity(R-l + x R) for u(0), the initial condition, in L-infinity(R). We provide some physical background for the study of this equation. In particular, g is assumed to be neither convex nor concave and k is a discontinuous function.