We consider a model of hyperbolic conservation laws with damping and show that the solutions tend to those of a nonlinear parabolic equation timeasymptotically. The hyperbolic model may be viewed as isentropic Euler equations with friction term added to the momentum equation to model gas flow through a porous media. In this case our result justifies Darcy's law timeasymptotically. Our model may also be viewed as an elastic model with damping.

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