A discrete BGK approximation for strongly degenerate parabolic problems with boundary conditions

We consider a class of BGK systems with a finite number of velocities, depending on a positive relaxation parameter, that approximate strongly degenerate hyperbolic–parabolic equations with initial boundary conditions. We prove a priori estimates for the solutions of the systems, showing that these functions converge towards the entropy solutions of strongly degenerate problems when the relaxation parameter goes to zero.