| Issue |
ESAIM: COCV
Volume 15, Number 1, January-March 2009
|
|
|---|---|---|
| Page(s) | 117 - 138 | |
| DOI | https://doi.org/10.1051/cocv:2008019 | |
| Published online | 23 January 2009 | |
Nash equilibrium for a multiobjective control problem related to wastewater management
1
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:
31
January
2007
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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