Convergence to nonlinear diffusion waves for solutions of the initial boundary problem to the hyperbolic conservation laws with damping

In this paper we consider a model of hyperbolic balance laws with damping o n the quarter plane (x, t) is an element of R+ x R+. By means of a suitable shift function, which will play a key role to overcome the difficulty of l arge boundary perturbations, we show that the IBVP solutions converge time- asymptotically to the shifted nonlinear diffusion wave solutions of the Cau chy problem to the nonlinear parabolic equation given by the related Darcy' s law. We obtain also the time decay rates, which are the optimal ones in t he L-2-sense. Our proof is based on the use of the classical energy method.