Porous media flow as the limit of a nonstrictly hyperbolic system of conservation laws

Abstract

We show here that the weak solutions of the quasilinear hyperbolic system

converge, as ∊ tends to zero, to the solution of the reduced problem

so that υ satisfies the nonlinear parabolic equation

The limiting procedure is carried out by using the theory of compensated compactness. Finally we obtain the existence of Lyapounov functionals for the limit parabolic equation as weak limit of the convex entropies as ∊ tends to zero for the corresponding hyperbolic system.