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

Emmanuelle Augeraud-Véron (), Catherine Choquet () and Éloïse Comte ()
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Catherine Choquet: University of La Rochelle
Éloïse Comte: University of La Rochelle

Journal of Optimization Theory and Applications, 2017, vol. 173, issue 3, No 12, 966 pages

Abstract: 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 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.

Keywords: Optimal control problem; Hydrogeological state equations; Nonlinearly coupled problem; Parabolic and elliptic PDEs; Global existence; Fixed point theorem; 49J20; 37N40; 76R99; 37N35 (search for similar items in EconPapers)
Date: 2017
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