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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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    1. Cyril Bourgeois & Pierre-Alain Jayet, 2016. "Regulation of relationships between heterogeneous farmers and an aquifer accounting for lag effects," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 60(1), pages 39-59, January.
    2. Camacho, Carmen & Pérez-Barahona, Agustín, 2015. "Land use dynamics and the environment," Journal of Economic Dynamics and Control, Elsevier, vol. 52(C), pages 96-118.
    3. Augeraud-Véron, Emmanuelle & Leandri, Marc, 2014. "Optimal pollution control with distributed delays," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 24-32.
    4. Anastasios Xepapadeas, 2011. "The Economics of Non-Point-Source Pollution," Annual Review of Resource Economics, Annual Reviews, vol. 3(1), pages 355-373, October.
    5. 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.
    6. Ralph Winkler, 2008. "Optimal control of pollutants with delayed stock accumulation," CER-ETH Economics working paper series 08/91, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
    7. Chahrazed Benosman & Bedr’Eddine Aïnseba & Arnaud Ducrot, 2015. "Optimization of Cytostatic Leukemia Therapy in an Advection–Reaction–Diffusion Model," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 296-325, October.
    8. Augeraud-Véron, Emmanuelle & Leandri, Marc, 2014. "Optimal pollution control with distributed delays," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 24-32.
    9. Lankoski, Jussi E. & Ollikainen, Markku, 2013. "Innovations in Nonpoint Source Pollution Policy—European Perspectives," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 28(3), pages 1-5.
    10. 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," AMSE Working Papers 1902, Aix-Marseille School of Economics, France.
    2. Boucekkine, Raouf & Ruan, Weihua & Zou, Benteng, 2023. "The irreversible pollution game," Journal of Environmental Economics and Management, Elsevier, vol. 120(C).
    3. Boucekkine, Raouf & Fabbri, Giorgio & Federico, Salvatore & Gozzi, Fausto, 2022. "Managing spatial linkages and geographic heterogeneity in dynamic models with transboundary pollution," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    4. 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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