# Nash equilibrium for a multiobjective control problem related to wastewater management

Néstor García-Chan; Rafael Muñoz-Sola; Miguel Ernesto Vázquez-Méndez

ESAIM: Control, Optimisation and Calculus of Variations (2009)

- Volume: 15, Issue: 1, page 117-138
- ISSN: 1292-8119

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topGarcía-Chan, Néstor, Muñoz-Sola, Rafael, and Vázquez-Méndez, Miguel Ernesto. "Nash equilibrium for a multiobjective control problem related to wastewater management." ESAIM: Control, Optimisation and Calculus of Variations 15.1 (2009): 117-138. <http://eudml.org/doc/250574>.

@article{García2009,

abstract = {
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).
},

author = {García-Chan, Néstor, Muñoz-Sola, Rafael, Vázquez-Méndez, Miguel Ernesto},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Optimal control; pointwise control; Nash equilibrium; existence; optimality conditions; numerical simulation; wastewater management; optimal control},

language = {eng},

month = {1},

number = {1},

pages = {117-138},

publisher = {EDP Sciences},

title = {Nash equilibrium for a multiobjective control problem related to wastewater management},

url = {http://eudml.org/doc/250574},

volume = {15},

year = {2009},

}

TY - JOUR

AU - García-Chan, Néstor

AU - Muñoz-Sola, Rafael

AU - Vázquez-Méndez, Miguel Ernesto

TI - Nash equilibrium for a multiobjective control problem related to wastewater management

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2009/1//

PB - EDP Sciences

VL - 15

IS - 1

SP - 117

EP - 138

AB -
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).

LA - eng

KW - Optimal control; pointwise control; Nash equilibrium; existence; optimality conditions; numerical simulation; wastewater management; optimal control

UR - http://eudml.org/doc/250574

ER -

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