Volume 15, Number 1, January-March 2009
|Page(s)||117 - 138|
|Published online||23 January 2009|
Nash equilibrium for a multiobjective control problem related to wastewater management
Departamento de Matemática Aplicada, Universidad de Santiago de Compostela, Facultad de Matemáticas, 15782 Santiago de Compostela, Spain. firstname.lastname@example.org; email@example.com
2 Departamento de Matemática Aplicada, Universidad de Santiago de Compostela, Escola Politécnica Superior, 27002 Lugo, Spain. firstname.lastname@example.org
Revised: 18 July 2007
Revised: 12 October 2007
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
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