The Zero Diffusion Limit For Nonlinear Hyperbolic System With Damping And Diffusion

In this paper, we consider Cauchy problem for some nonlinear hyperbolic system with damping and diffusion. Through constructing a correct function which is used to eliminate the layer at infinite and using the energy method, we establish the global existence if the initial data is a small perturbation around the corresponding linear diffusion waves. Furthermore, we study the zero diffusion limit. Precisely, we show that the solution sequence converges to the corresponding hyperbolic system as the diffusion parameter tends to zero.