Stabilization of Flows Through Porous Media

descriptionPublicationkeyboard_double_arrow_right Article 01 Mar 1979 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Mathematical Analysis, volume 10, pages 237-246 (issn: 0036-1410, eissn: 1095-7154,

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Authors: Gilding, B. H.;

doi: 10.1137/0510022

Stabilization of Flows Through Porous Media

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Abstract

Let $u(x,t)$ be the solution of the Cauchy–Dirichlet problem for the porous media equation in one space dimension in the quarter-plane $(0,\infty ) \times (0,\infty )$. An estimate is obtained for the asymptotic behaviour of $u(t,x)$ as $t \to \infty $, in terms of the prescribed lateral boundary value of u. The paper is an enlargement on a result of Peletier [SIAM J. Appl. Math, 1971].

Keywords

Diffusion and convection, similarity solution, Flows in porous media; filtration; seepage, Asymptotic behavior of solutions to PDEs, polytropic gas, stabilization, flows through porous media, non-linear diffusion equation

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