Optimal Control for a Groundwater Pollution Ruled by a Convection‐Diffusion‐Reaction Problem

We consider an optimal control problem of underground water contaminated by agricultural pollution. The economical intertemporal objective takes into account the trade‐off between fertilizer use and cleaning costs. It is constrained by a hydrogeological model for the spread of the pollution in the aquifer. This model consists in a parabolic partial differential equation which is nonlinearly coupled through the dispersion tensor with an elliptic equation, in a three‐dimensional domain. We prove the existence of a global optimal solution under various regularity assumptions and for a wide variety of boundary conditions. We also provide an asymptotic controllability result.