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Asymptotic expansions of the pressure and the free boundary for flows through porous media

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Abstract

In this paper we discuss the free boundary value problem for the pressure head u of a compressible fluid flowing through a homogeneous porous medium. This process is governed by the partial differential equation ∈∂tu-∂ 2x u=0, where ∈ is proportional to the compressibility of the fluid. We shall show that the pressure as well as the free boundary converge to the corresponding stationary solutions when ∈ tends to zero and shall furthermore estimate the error in terms of powers of ∈. Roughly speaking in the case of water, for example, this means that if we neglect its compressibility, which indeed is very small, we can estimate the error.

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  1. Institut fÜr Angewandte Mathematik, der Universität Bonn, Wegelerstr. 6, D - 5300, Bonn

    Dietmar Kröner

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  1. Dietmar Kröner
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Kröner, D. Asymptotic expansions of the pressure and the free boundary for flows through porous media. Manuscripta Math 44, 131–153 (1983). https://doi.org/10.1007/BF01166079

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  • DOI: https://doi.org/10.1007/BF01166079

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