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On the optimal control of coefficients in elliptic problems. Application to the optimization of the head slider

Published online by Cambridge University Press:  15 December 2004

Ionel Ciuperca ,
Mohamed El Alaoui Talibi  and
Mohammed Jai
Ionel Ciuperca
Affiliation:
CNRS-UMR 5585 Université Lyon 1, MAPLY, 101, 69622 Villeurbanne Cedex, France.
Mohamed El Alaoui Talibi
Affiliation:
Department of Mathematics, Fac. Sciences Semlalia, 40000 Marrakech, Morocco.
Mohammed Jai
Affiliation:
CNRS-UMR 5585, INSA de LYON, Mathématiques Bât. Leonard de Vinci, 69621 Villeurbanne, France; [email protected]
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Abstract

We consider an optimal control problem for a class of non-linearelliptic equations. A result of existence and uniqueness of the state equation is proven under weaker hypotheses than in theliterature. We also prove the existence of an optimalcontrol. Applications to some lubrication problems and numericalresults are given.

Keywords

Compressible Reynolds lubrication equationoptimal control problemsShauder fixed point theorem.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 11 , Issue 1 , January 2005 , pp. 102 - 121
Copyright
© EDP Sciences, SMAI, 2005

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References

A. Bensoussan, J.L. Lions and G. Papanicolaou, Asymptotic analysis for periodic structure. North-Holland (1978).
Burgdorfer, B., The influence of the molecular mean free path on the performance of hydrodynamic gas lubricated bearings. ASME J. basic Engineer. 81 (1959) 99–100.
Chipot, M. and Luskin, M., Existence and uniqueness of solutions to the compressible Reynolds lubrication equation. SIAM J. Math. Anal. 17 (1986) 1390–1399. CrossRef
J.I. Diaz and J.I. Tello, On a problem lacking a classical solution in lubrication theory, in Actas del XV-CEDYA, Vigo II (1997) 429–434.
L.C. Evans and R.F. Gariepy, Measure theory and fine properties of functions. Stud. Adv. Math. CRC Press (1992).
D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order. Springer-Verlag, Berlin, second edition (1983).
Grigor'ev, B.S., Lupulyak, S.V. and Shinder, Yu.K., Solvability of the reynolds equation of gas lubrication. J. Math. Sci. 106 (2001) 2925–2928. CrossRef
Jai, M., Existence and uniqueness of solutions of the parabolic nonlinear compressible Reynolds lubrication equation. Nonlinear Anal. 43 (2001) 655–682. CrossRef
D. Kinderlehrer and G. Stampacchia, An introduction to variational inequalities and their applications. Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York (1980).
Rayleigh, L., Notes on the Theory of Lubrication. Phylosophical Magazine 35 (1918) 1–12.
Robert, M.P., Optimization of self-acting gas bearings for maximum static siffness. ASME J. Appl. Mech. 57 (1990) 758–761. CrossRef
S.M. Rodhe and G.T. McAllister, On the optimization of fluid film bearings. Proc. Roy. Soc. London A 351 (1976) 481–497. CrossRef
Tello, J. I., Regularity of solutions to a lubrication problem with discontinuous separation data. Nonlinear Anal. 53 (2003) 1167–1177. CrossRef