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Fluid flow in partially saturated porous media. (English) Zbl 0608.76081

Semigroups, theory and applications, Vol. 1, Pap. Autumn Course Int. Cent. Theor. Phys., Miramare (Trieste)/Italy 1984, Pitman Res. Notes Math. Ser. 141, 28-35 (1986).
[For the entire collection see Zbl 0585.00006.]
The paper gives an analytical solution of the fluid flow in a partially saturated porous medium. The equation of continuity together with Darcy’s law leads to an equation which is of elliptic type in the saturated region and parabolic type in the unsaturated region. Thus it is a discontinuous problem.
Only the one dimensional case is considered. The interface is a moving boundary which leads to more complication. However, some solutions are obtained by many manipulations. The paper will be more interesting to the researchers in the area of partial differential equations.
Reviewer: G.Paria

MSC:

76S05 Flows in porous media; filtration; seepage
35M99 Partial differential equations of mixed type and mixed-type systems of partial differential equations
35A35 Theoretical approximation in context of PDEs

Citations:

Zbl 0585.00006