ESAIM: COCV
DOI: 10.1051/cocv:2008019

Nash equilibrium for a multiobjective control problem related to wastewater management

Néstor García-Chan¹, Rafael Muñoz-Sola¹ and Miguel Ernesto Vázquez-Méndez<sup>2

1</sup>  Departamento de Matemática Aplicada, Universidad de Santiago de Compostela, Facultad de Matemáticas, 15782, Santiago de Compostela, Spain; netog-g@hotmail.com; rafams@usc.es
²  Departamento de Matemática Aplicada, Universidad de Santiago de Compostela, Escola Politécnica Superior, 27002, Lugo, Spain; ernesto@usc.es

(Received January 31, 2007. Revised July 18, 2007 and October 12, 2007. Published online March 6, 2008.)

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).

Mathematics Subject Classification. 49J20, 49K20, 90C29, 91B76

Key words: Optimal control, pointwise control, Nash equilibrium, existence, optimality conditions, numerical simulation, wastewater management


© EDP Sciences, SMAI 2008