On nonstationary flow through porous media (Q801766)

The authors deal with saturated-unsaturated flow of an incompressible fluid through a porous medium in the case of time dependent water levels [see also \textit{A. Torelli}, Boll. Unione Mat. Ital., IV. Ser. 11, 559-570 (1975; Zbl 0331.76058); \textit{G. Gilardi}, Commun. Partial Differ. Equations 4, 1099-1122 (1979; Zbl 0426.35096); the third author, Ann. Mat. Pura Appl., IV. Ser. 124, 293-320 (1980; Zbl 0445.76078)]. The existence of the corresponding weak solution is obtained. Strong convergence of the saturation in one space dimension is proved.