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Nash equilibrium for a multiobjective control problem related to wastewater management

Published online by Cambridge University Press:  23 January 2009

Néstor García-Chan ,
Rafael Muñoz-Sola  and
Miguel Ernesto Vázquez-Méndez
Néstor García-Chan
Affiliation:
Departamento de Matemática Aplicada, Universidad de Santiago de Compostela, Facultad de Matemáticas, 15782 Santiago de Compostela, Spain. netog_g@hotmail.com; rafams@usc.es
Rafael Muñoz-Sola
Affiliation:
Departamento de Matemática Aplicada, Universidad de Santiago de Compostela, Facultad de Matemáticas, 15782 Santiago de Compostela, Spain. netog_g@hotmail.com; rafams@usc.es
Miguel Ernesto Vázquez-Méndez
Affiliation:
Departamento de Matemática Aplicada, Universidad de Santiago de Compostela, Escola Politécnica Superior, 27002 Lugo, Spain. ernesto@usc.es
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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).


Keywords

Optimal controlpointwise controlNash equilibriumexistenceoptimality conditionsnumerical simulationwastewater management
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 15 , Issue 1 , January 2009 , pp. 117 - 138
Copyright
© EDP Sciences, SMAI, 2008

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