Optimal Buffer Zone for the Control of Groundwater Pollution from Agricultural Activities

Abstract

We consider an optimal control model of groundwater pollution due to agricultural activities, the objective of the optimal manager being the optimization of the trade-off between the fertilizer use and the cleaning costs. The size of a buffer zone defined around the water production sites for limiting pollution effects may also be chosen by the manager. The spread of the pollution from crops to captation wells is modeled using a convection–diffusion–reaction equation. The main hydrogeological features of the dynamics are taken into account: the process is convection-dominated, dispersion effects are included, generic nonlinear reaction terms are considered. The existence and the uniqueness of the optimal solution is proven. Using asymptotic analysis, we then rigorously prove that a one-dimensional static model can be substituted to the full dynamic 3D model for the long time study of the optimal solution. We prove that this new optimal control problem is also well-posed. All these theoretical results are used for characterizing the optimal buffer zone.