Optimal Control for a Groundwater Pollution Ruled by a Convection–Diffusion–Reaction Problem
Language
EN
Article de revue
This item was published in
Journal of Optimization Theory and Applications. 2016-10-03, vol. 173, n° 3, p. 941-966
English Abstract
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 ...Read more >
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.Read less <
English Keywords
Optimal control problem
Hydrogeological state equations
Nonlinearly coupled problem
Parabolic and elliptic PDEs
Global existence
Fixed point theorem