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Zbl 0981.49003
El Alaoui Talibi, Mohamed; El Kacimi, Abdellah
Control by coefficients in the Elrod-Adams model. (Contrôle par les coefficients dans le modèle Elrod-Adams.) (English, French)
[J] ESAIM, Control Optim. Calc. Var. 6, 97-118 (2001). ISSN 1292-8119; ISSN 1262-3377/e

Summary: 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 with 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.

MSC 2000:: *49J40 Variational methods including variational inequalities
76D08 Lubrication theory
76M30 Variational methods
35R35 Free boundary problems for PDE
35J85 Unilateral problems; variational inequalities (elliptic type)

Keywords: optimal control; elastohydrodynamic identification of coefficients; lubrification; nonlinear elliptic problems; regularization

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