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Nash equilibrium for a multiobjective control problem related to wastewater management

Néstor García-Chan;  Rafael Muñoz-Sola;  Miguel Ernesto Vázquez-Méndez — 2009

ESAIM: Control, Optimisation and Calculus of Variations

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).


Application of the optimal control theory to the wastewater elimination problem.

Lino José Alvarez-Vázquez;  Alfredo Bermúdez;  Aurea Martínez;  Carmen Rodríguez;  Miguel Ernesto Vázquez-Méndez — 2002

RACSAM

The main goal of this paper is to show some applications of the optimal control theory to the wastewater elimination problem. Firstly, we deal with the numerical simulation of a given situation. We present a suitable mathematical model, propose a method to solve it and show the numerical results for a realistic situation in the (Spain). Secondly, in the same framework of wastewater elimination problem, we pose two economic-environmental problems which can be formulated as constrained optimal control...

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