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).
Classification : 49J20, 49K20, 90C29, 91B76
Mots clés : optimal control, pointwise control, Nash equilibrium, existence, optimality conditions, numerical simulation, wastewater management
@article{COCV_2009__15_1_117_0,
author = {Garc\'\i a-Chan, N\'estor and Mu\~noz-Sola, Rafael and V\'azquez-M\'endez, Miguel Ernesto},
title = {Nash equilibrium for a multiobjective control problem related to wastewater management},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {117--138},
publisher = {EDP-Sciences},
volume = {15},
number = {1},
year = {2009},
doi = {10.1051/cocv:2008019},
zbl = {1155.49002},
mrnumber = {2488571},
language = {en},
url = {http://www.numdam.org/item/COCV_2009__15_1_117_0/}
}
García-Chan, Néstor; Muñoz-Sola, Rafael; Vázquez-Méndez, Miguel Ernesto. Nash equilibrium for a multiobjective control problem related to wastewater management. ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 1, pp. 117-138. doi : 10.1051/cocv:2008019. http://www.numdam.org/item/COCV_2009__15_1_117_0/
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