THE ZERO DIFFUSION LIMIT FOR NONLINEAR HYPERBOLIC SYSTEM WITH DAMPING AND DIFFUSION

Abstract

We consider the Cauchy problem for a nonlinear hyperbolic system with damping and diffusion. Thanks to a suitably constructed corrector function, we can eliminate the layer at infinity and by using the energy method we establish the global existence of solutions if the initial data is a small perturbation around the corresponding linear diffusion waves. Furthermore, we study the zero diffusion limit and, precisely, we show that the sequence of solutions converges to the corresponding hyperbolic system as the diffusion parameter tends to zero.