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Lp-Convergence Rate to Nonlinear Diffusion Waves for p-System with Damping

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In this paper, we study the p-system with frictional damping and show that the solutions time-asymptotically tend to the nonlinear diffusion waves governed by the classical Darcy's law. By introducing an approximate Green function, we obtain the optimal Lp, 2p+∞, convergence rate of the solution, which is a perturbation of the nonlinear diffusion wave, to the hyperbolic system. Copyright 2000 Academic Press.

Keywords: Lp estimate; approximate Green function; nonlinear diffusion wave; p-system with damping

Document Type: Research Article

Affiliations: 1: School of Political Science and Economics, Waseda University 2: Department of Mathematics, Wuhan University 3: Department of Mathematics, City University of Hong Kong

Publication date: February 1, 2000

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