Summary
Saturated-unsaturated flow of an incompressible fluid through a porous medium is considered in the case of time-dependent water levels. This corresponds to coupling the mass conservation law with a continuous constitutive condition between water content and pressure. An existence result for the corresponding weak formulation is proved. Finally we study the limit as the constitutive relation degenerates into a maximal monotone graph.
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This work was supported by the Deutsche Forschungsgemeinschaft through Sonderforschungsbereich 123 (Heidelberg).
On leave from: Istituto di Analisi Numerica del C.N.R., Corso C. Alberto 5 - I 27100 Pavia (Italy).
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Alt, H.W., Luckhaus, S. & Visintin, A. On nonstationary flow through porous media. Annali di Matematica pura ed applicata 136, 303–316 (1984). https://doi.org/10.1007/BF01773387
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DOI: https://doi.org/10.1007/BF01773387