Nonstationary filtration in partially saturated porous media
Abstract
From the mathematical formulation of a one dimensional flow through a partially saturated porous medium, a nonlinear free boundary problem is posed, the boundary being between the saturated and the unsaturated regions in the medium. In particular, an equation which is parabolic in the unsaturated part of the domain and elliptic in the saturated part is obtained. Existence, uniqueness, a maximum principle, and regularity properties are proved for weak solutions of a CauchyDirichlet problem in the cylinder (x,t) : 0 or = X or = 1, T or = 0 and the nature, in particular the regularity, of the free boundary is discussed. Finally, it is shown that solutions of a large class of CauchyDirichlet problems converge towards a stationary solution as t tends to infinity. Estimates are given for this rate of convergence.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 May 1979
 Bibcode:
 1979STIN...8029631V
 Keywords:

 Elliptic Differential Equations;
 Flow Theory;
 Parabolic Differential Equations;
 Porous Boundary Layer Control;
 Cauchy Problem;
 Convergence;
 Dirichlet Problem;
 Existence Theorems;
 Fluid Flow;
 Free Boundaries;
 Maximum Principle;
 Nonlinear Equations;
 One Dimensional Flow;
 Water Tables;
 Fluid Mechanics and Heat Transfer