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Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping. (English) Zbl 0763.35058

Summary: We consider a model of hyperbolic conservation laws with damping and show that the solutions tend to those of a nonlinear parabolic equation time- asymptotically. 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 time-asymptotically. Our model may also be viewed as an elastic model with damping.

MSC:

35L65 Hyperbolic conservation laws
35Q35 PDEs in connection with fluid mechanics
76S05 Flows in porous media; filtration; seepage
35B40 Asymptotic behavior of solutions to PDEs
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References:

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