Qualitative mathematical analysis of the Richards equation

B.H. Gilding

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    Abstract

    The Richards equation is widely used as a model for the flow of water in unsaturated soils. For modelling one-dimensional flow in a homogeneous soil, this equation can be cast in the form of a specific nonlinear partial differential equation with a time derivative and one spatial derivative. This paper is a survey of recent progress in the pure mathematical analysis of this last equation. The emphasis is on the interpretation of the results of the analysis. These are explained in terms of the qualitative behaviour of the flow of water in an unsaturated soil which is described by the Richards equation.
    Original languageEnglish
    Pages (from-to)651-656
    Number of pages6
    JournalTransport in porous media
    Volume6
    Issue number5-6
    DOIs
    Publication statusPublished - 1991

    Keywords

    • advection
    • Partial differential equation
    • unsaturated soils
    • wetting-fronts
    • qualitative behaviour
    • IR-85880
    • Fokker-Planck
    • Diffusion
    • Non-linear
    • METIS-140651
    • Mathematical analysis

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