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Pollution agricole des ressources en eau : approches couplées hydrogéologique et économique

Abstract : This work is devoted to water ressources pollution control. We especially focus on the impact of agricultural fertilizer on water quality, by combining economical and hydrogeological modeling. We define, on one hand, the spatio-temporal objective, taking into account the trade off between fertilizer use and the cleaning costs. On an other hand, we describe the pollutant transport in the underground (3D in space) by a nonlinear system coupling a parabolic partial differential equation (reaction-advection-dispersion) with an elliptic one in a bounded domain. We prove the global existence of the solution of the optimal control problem. The uniqueness is proved by asymptotic analysis for the effective problem taking into account the low concentration fertilizer. We define the optimal necessary conditions and the adjoint problem associated to the model. Some analytical results are provided and illustrated. We extend these results within the framework of game theory, where several players are involved, and we prove the existence of a Nash equilibrium. Finally, this work is illustrated by numerical results (2D in space), produced by coupling a Mixed Finite Element scheme with a nonlinear conjugate gradient algorithm.
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Eloïse Comte. Pollution agricole des ressources en eau : approches couplées hydrogéologique et économique. Optimisation et contrôle [math.OC]. Université de La Rochelle, 2017. Français. ⟨NNT : 2017LAROS029⟩. ⟨tel-01804984⟩

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