Optimal decay rates of solutions to hyperbolic conservation laws with damping

In this paper, we are concerned with the asymptotic behavior of solutions to the system of hyperbolic conservation laws with damping. In particular, a system includes compressible Euler equations with damping, Ml-model, etc. Under some smallness conditions on initial perturbations, we prove that the solutions to the Cauchy problem of the system globally exist and time-asymptotically converge to corresponding equilibrium state, and further give the optimal convergence rate. The approach adopted is the technical time-weighted energy method combined with the Green's function method.