On the convergence of the parabolic approximation of a conservation law in several space dimensions

The authors give a proof of the convergence of the solution of the parabolic approximation u(t)(epsilon) + divf(x, t, u(epsilon)) = epsilon Delta u(epsilon) towards the entropic solution of the scalar conservation law u(t) + divf(x, t, u) = 0 in several space dimensions. For any initial condition u(0) is an element of L-infinity(R-N) and for a large class of flux f, they also prove the strong converge in any L-loc(p) space, using the notion of entropy process solution, which is a generalization of the measure-valued solutions of DiPerna.