A mathematical approach to a forest-impact problem

In this article a mathematical model of forests impact on aquifers is proposed. This phenomenon is the lowering of the groundwater table under areas covered by trees. The model includes a boundary-value problem with contact and free-boundary conditions. A variational formulation of this problem, which is a quasi-variational inequality, is obtained. Its equivalence with the original problem is proved; existence and uniqueness results are obtained. A numerical example of the model is given.