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Contrôle par les coefficients dans le modèle elrod-adams

Published online by Cambridge University Press:  15 August 2002

Mohamed El Alaoui Talibi  and
Abdellah El Kacimi
Mohamed El Alaoui Talibi
Affiliation:
Faculté des Sciences Semalila, Département de Mathématiques, BP. 2930 Marrakech, Maroc ; elalaoui@ucam.ac.ma.
Abdellah El Kacimi
Affiliation:
Faculté des Sciences Semalila, Département de Mathématiques, BP. 2930 Marrakech, Maroc ; elalaoui@ucam.ac.ma.
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Abstract

The purpose of this paper is to study a control by coefficients problem issued from the elastohydrodynamic lubrication. The control variable is the film thickness.The cavitation phenomenon takes place and described by the Elrod-Adams model, suggested in preference to the classical variational inequality due to its ability to describe input and output flow. The idea is to use the penalization in the state equation  by approximating the Heaviside graph whith a sequence of monotone and regular functions. We derive a necessary condition for the regularized problem,  then we establish estimates of the state and the adjoint state in the one dimensional case. Next we pass to the limit.

Keywords

Contrôle optimalidentification des coefficientslubrificationproblème elliptique non linéairerégularisation.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 6 , 2001 , pp. 97 - 118
Copyright
© EDP Sciences, SMAI, 2001

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