Nash equilibrium for a multiobjective control problem related to wastewater management
García-Chan, Néstor ; Muñoz-Sola, Rafael ; Vázquez-Méndez, Miguel Ernesto1
1 Departamento de Matemática Aplicada, Universidad de Santiago de Compostela, Escola Politécnica Superior, 27002 Lugo, Spain.
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 : 10.1051/cocv:2008019
Classification : 49J20, 49K20, 90C29, 91B76
Mots-clés : optimal control, pointwise control, Nash equilibrium, existence, optimality conditions, numerical simulation, wastewater management
García-Chan, Néstor  ; Muñoz-Sola, Rafael  ; Vázquez-Méndez, Miguel Ernesto 1

1 Departamento de Matemática Aplicada, Universidad de Santiago de Compostela, Escola Politécnica Superior, 27002 Lugo, Spain. 
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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/articles/10.1051/cocv:2008019/

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