Abstract
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.
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Communicated by A. Jaffe
Research supported in part by Energy Dept. grant DEFG 02-88-ER25053
Research supported in part by NSF grant DMS 90-0226 and Army grant DAAL 03-91-G0017
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Hsiao, L., Liu, TP. Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping. Commun.Math. Phys. 143, 599–605 (1992). https://doi.org/10.1007/BF02099268
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DOI: https://doi.org/10.1007/BF02099268