Some properties of the solution of a filtration problem in partially saturated porous media
A filtration problem with second initial-boundary value in partially saturated porous media is considered. One of the difficulties of this problem is the appearance of the free boundary which separates the saturated and unsaturated regions. The uniqueness and the existence of the weak solution of the problem is proved. The existence and the continuity of the free surface is proved under certain conditions. In the last part a maximum principle for the weak solution is established, from which a time-limit existence of this solution is obtained.
scientific article; zbMATH DE number 3956708