Large Time Behavior of Solutions for Nonlinear Hyperbolic System with Low-Order Dissipation

We consider a model of hyperbolic conservation laws with damping and show that the solutions tend to those of a nonlinear diffusion equation with a rate of ty1r2 time-asymptotically. The hyperbolic model may be viewed as isentropic Euler equations with friction term added to the momentum equation to model fluid flow in a pipe