The infiltration problem with constant rate in partially saturated porous media (Q1077294)

The infiltration problem with constant rate in partially saturated porous media is presented. The weak solution of the problem is defined in the same way as in the well known paper of \textit{O. Oleinik}, \textit{A. Kalashnikov} and \textit{J. Chzhou}, Izv. Akad. Nauk SSSR, Ser. Mat. 22, 667-704 (1958; Zbl 0093.103). The existence of the weak solution is proved using a sequence with approximate the initial conditions and physical quantities which characterize the flow. In the last part it is proved that the initially saturated part will fall down to completely unsaturated state with the increase of time.