Contrôle par les coefficients dans le modèle elrod-adams

Mohamed El Alaoui Talibi; Abdellah El Kacimi

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 6, page 97-118
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Mohamed El Alaoui Talibi, and El Kacimi, Abdellah. "Contrôle par les coefficients dans le modèle elrod-adams." ESAIM: Control, Optimisation and Calculus of Variations 6 (2010): 97-118. <http://eudml.org/doc/197320>.

@article{MohamedElAlaouiTalibi2010,
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. },
author = {Mohamed El Alaoui Talibi, El Kacimi, Abdellah},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Contrôle optimal; identification des coefficients; lubrification; problème elliptique non linéaire; régularisation.; optimal control; elastohydrodynamic identification of coefficients; nonlinear elliptic problems; regularization},
language = {eng},
month = {3},
pages = {97-118},
publisher = {EDP Sciences},
title = {Contrôle par les coefficients dans le modèle elrod-adams},
url = {http://eudml.org/doc/197320},
volume = {6},
year = {2010},
}

TY - JOUR
AU - Mohamed El Alaoui Talibi
AU - El Kacimi, Abdellah
TI - Contrôle par les coefficients dans le modèle elrod-adams
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 6
SP - 97
EP - 118
AB - 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.
LA - eng
KW - Contrôle optimal; identification des coefficients; lubrification; problème elliptique non linéaire; régularisation.; optimal control; elastohydrodynamic identification of coefficients; nonlinear elliptic problems; regularization
UR - http://eudml.org/doc/197320
ER -

References

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  13. E. Casas, O. Kavian et J.P. Puel, Optimal control of an ill-posed elliptic semilinear equation whith an exponential non linearity. ESAIM: COCV3 (1998) 361-380.  Zbl0911.49003
  14. G. Elrod H. et M.L. Adams, A computer program for cavitation, in st LEEDS LYON symposium on cavitation and related phenomena in lubrication, I.M.E. (1974).  
  15. D. Gilbarg et N.S. Trudinger, Elliptic Partial Differential Equations of second Order. Springer-Verlag (1983).  Zbl0562.35001
  16. O.A. Ladyzhenskaya et N.N. Ural'tseva, Linear and quasilinear elliptic equations. Academic Press (1968).  
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  19. G. Stampachia et D. Kinderleher, An introduction to variational inequalities and applications. Academic Press (1980).  

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