Volume 17, Number 3, July-September 2011
|Page(s)||722 - 748|
|Published online||23 April 2010|
Departamento de Matemática Aplicada II,
E.T.S.I. Telecomunicación, Universidad de Vigo, 36310 Vigo,
Spain. email@example.com; firstname.lastname@example.org
2 Departamento de Matemática Aplicada, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15706 Santiago, Spain. email@example.com
Revised: 3 September 2009
Revised: 21 January 2010
We consider a time optimal control problem arisen from the optimal management of a bioreactor devoted to the treatment of eutrophicated water. We formulate this realistic problem as a state-control constrained time optimal control problem. After analyzing the state system (a complex system of coupled partial differential equations with non-smooth coefficients for advection-diffusion-reaction with Michaelis-Menten kinetics, modelling the eutrophication processes) we demonstrate the existence of, at least, an optimal solution. Then we present a detailed derivation of a first order optimality condition (involving the corresponding adjoint systems) characterizing these optimal solutions. Finally, a numerical example is shown.
Mathematics Subject Classification: 35D05 / 49J20 / 93C20
Key words: Time optimal control / partial differential equations / optimality conditions / existence / bioreactor
© EDP Sciences, SMAI, 2010
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