Nash equilibrium for a multiobjective control problem related to wastewater management
ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 1, pp. 117-138.

This paper is concerned with mathematical modelling in the management of a wastewater treatment system. The problem is formulated as looking for a Nash equilibrium of a multiobjective pointwise control problem of a parabolic equation. Existence of solution is proved and a first order optimality system is obtained. Moreover, a numerical method to solve this system is detailed and numerical results are shown in a realistic situation posed in the estuary of Vigo (Spain).

DOI : https://doi.org/10.1051/cocv:2008019
Classification : 49J20,  49K20,  90C29,  91B76
Mots clés : optimal control, pointwise control, Nash equilibrium, existence, optimality conditions, numerical simulation, wastewater management
@article{COCV_2009__15_1_117_0,
     author = {Garc\'\i a-Chan, N\'estor and Mu\~noz-Sola, Rafael and V\'azquez-M\'endez, Miguel Ernesto},
     title = {Nash equilibrium for a multiobjective control problem related to wastewater management},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {117--138},
     publisher = {EDP-Sciences},
     volume = {15},
     number = {1},
     year = {2009},
     doi = {10.1051/cocv:2008019},
     zbl = {1155.49002},
     mrnumber = {2488571},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2009__15_1_117_0/}
}
García-Chan, Néstor; Muñoz-Sola, Rafael; Vázquez-Méndez, Miguel Ernesto. Nash equilibrium for a multiobjective control problem related to wastewater management. ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 1, pp. 117-138. doi : 10.1051/cocv:2008019. http://www.numdam.org/item/COCV_2009__15_1_117_0/

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