MATHEMATICAL ANALYSIS OF A SUBSURFACE FLOW MODEL.

The purpose of this article is the mathematical analysis of a new class of models to describe the flow in shallow aquifers, as alternatives to the 3d-Richards model. This type of models was introduced in a previous work and consists of the coupling of an almost 1d vertical flow in the upper part of the aquifer with a 2d horizontal flow in the lower part. These two regions being separated by a time-dependent interface, an unknown of the problem. A result of existence of weak solutions is proved for a very general form of the hydraulic conductivity (anisotropic case). The strategy is based on the classical framework of parabolic equations in non-cylindrical domains. It also exploits the compressibility of the fluid to overcome the difficulty associated with the degeneracy in the time derivative term of Richards equation. [ABSTRACT FROM AUTHOR]