Dans ce papier, nous étudions un problème de contrôle par les coefficients issu de la lubrification élastohydrodynamique. La variable de contrôle est l’épaisseur du fluide. Le phénomène de cavitation est pris en compte par le modèle Elrod-Adams, connu pour ses performances dans la conservation des débits d’entrée et de sortie. L’idée est de régulariser dans l’équation d’état le graphe d’Heaviside, en l’approchant par une suite de fonctions monotones et régulières. Nous dérivons les conditions d’optimalité...
We consider an optimal control problem for a class of non-linear elliptic equations. A result of existence and uniqueness of the state equation is proven under weaker hypotheses than in the literature. We also prove the existence of an optimal control. Applications to some lubrication problems and numerical results are given.
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 consider an optimal control problem for a class of non-linear
elliptic equations. A result of existence and uniqueness
of the state equation is proven under weaker hypotheses than in the
literature. We also prove the existence of an optimal
control. Applications to some lubrication problems and numerical
results are given.
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