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

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  • Emmanuelle Augeraud-Véron

    () (University of La Rochelle)

  • Catherine Choquet

    () (University of La Rochelle)

  • Éloïse Comte

    () (University of La Rochelle)

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.

Suggested Citation

  • Emmanuelle Augeraud-Véron & Catherine Choquet & Éloïse Comte, 2017. "Optimal Control for a Groundwater Pollution Ruled by a Convection–Diffusion–Reaction Problem," Journal of Optimization Theory and Applications, Springer, vol. 173(3), pages 941-966, June.
    • Handle: RePEc:spr:joptap:v:173:y:2017:i:3:d:10.1007_s10957-016-1017-8
    DOI: 10.1007/s10957-016-1017-8
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    References listed on IDEAS

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    4. Augeraud-Véron, Emmanuelle & Leandri, Marc, 2014. "Optimal pollution control with distributed delays," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 24-32.
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    7. Javier de Frutos & Guiomar Martín-Herrán, 2016. "Pollution control in a multiregional setting: a differential game with spatially distributed controls," Gecomplexity Discussion Paper Series 201601, Action IS1104 "The EU in the new complex geography of economic systems: models, tools and policy evaluation", revised Jan 2016.
    8. Brock, William & Xepapadeas, Anastasios, 2008. "Diffusion-induced instability and pattern formation in infinite horizon recursive optimal control," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 2745-2787, September.
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    Cited by:

    1. Emmanuelle Augeraud-Véron & Raouf Boucekkine & Vladimir Veliov, 2019. "Distributed Optimal Control Models in Environmental Economics: A Review," Working Papers halshs-01982243, HAL.
    2. de Frutos, Javier & Martín-Herrán, Guiomar, 2019. "Spatial vs. non-spatial transboundary pollution control in a class of cooperative and non-cooperative dynamic games," European Journal of Operational Research, Elsevier, vol. 276(1), pages 379-394.

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