Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping |
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| Authors: | Ling Hsiao Tai-Ping Liu |
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| Institution: | (1) Institute of Mathematics, Academia Sinica, Beijing, China;(2) Department of Mathematics, Stanford University, 94305-2125 Stanford, CA, USA |
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| 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.Research supported in part by Energy Dept. grant DEFG 02-88-ER25053Research supported in part by NSF grant DMS 90-0226 and Army grant DAAL 03-91-G0017 |
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