Convergence of hydrodynamical limits for generalized carleman models

We consider the initial-boundary value problem for a 2-speed system of first order semilinear hyperbolic equations. We establish the existence of global weak solutions in L¹ by the theory of nonlinear contraction semigroups. Using the monotone method and the div-curl lemma, we investigate the hydrodynamical limits of the solutions of the hyperbolic systems and show that the limits verify the doubly nonlinear parabolic equations.