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.
Mots-clés : compressible Reynolds lubrication equation, optimal control problems, Shauder fixed point theorem
@article{COCV_2005__11_1_102_0,
author = {Ciuperca, Ionel and El Alaoui Talibi, Mohamed and Jai, Mohammed},
title = {On the optimal control of coefficients in elliptic problems. {Application} to the optimization of the head slider},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {102--121},
publisher = {EDP-Sciences},
volume = {11},
number = {1},
year = {2005},
doi = {10.1051/cocv:2004029},
mrnumber = {2110616},
zbl = {1101.49004},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2004029/}
}
TY - JOUR AU - Ciuperca, Ionel AU - El Alaoui Talibi, Mohamed AU - Jai, Mohammed TI - On the optimal control of coefficients in elliptic problems. Application to the optimization of the head slider JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2005 SP - 102 EP - 121 VL - 11 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2004029/ DO - 10.1051/cocv:2004029 LA - en ID - COCV_2005__11_1_102_0 ER -
%0 Journal Article %A Ciuperca, Ionel %A El Alaoui Talibi, Mohamed %A Jai, Mohammed %T On the optimal control of coefficients in elliptic problems. Application to the optimization of the head slider %J ESAIM: Control, Optimisation and Calculus of Variations %D 2005 %P 102-121 %V 11 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2004029/ %R 10.1051/cocv:2004029 %G en %F COCV_2005__11_1_102_0
Ciuperca, Ionel; El Alaoui Talibi, Mohamed; Jai, Mohammed. On the optimal control of coefficients in elliptic problems. Application to the optimization of the head slider. ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 1, pp. 102-121. doi : 10.1051/cocv:2004029. http://www.numdam.org/articles/10.1051/cocv:2004029/
[1] , and, Asymptotic analysis for periodic structure. North-Holland (1978). | MR | Zbl
[2] , The influence of the molecular mean free path on the performance of hydrodynamic gas lubricated bearings. ASME J. basic Engineer. 81 (1959) 99-100.
[3] and, Existence and uniqueness of solutions to the compressible Reynolds lubrication equation. SIAM J. Math. Anal. 17 (1986) 1390-1399. | Zbl
[4] and, On a problem lacking a classical solution in lubrication theory, in Actas del XV-CEDYA, Vigo II (1997) 429-434. | Zbl
[5] and, Measure theory and fine properties of functions. Stud. Adv. Math. CRC Press (1992). | MR | Zbl
[6] and, Elliptic partial differential equations of second order. Springer-Verlag, Berlin, second edition (1983). | MR | Zbl
[7] , and, Solvability of the reynolds equation of gas lubrication. J. Math. Sci. 106 (2001) 2925-2928.
[8] , Existence and uniqueness of solutions of the parabolic nonlinear compressible Reynolds lubrication equation. Nonlinear Anal. 43 (2001) 655-682. | Zbl
[9] and, An introduction to variational inequalities and their applications. Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York (1980). | MR | Zbl
[10] , Notes on the Theory of Lubrication. Phylosophical Magazine 35 (1918) 1-12.
[11] , Optimization of self-acting gas bearings for maximum static siffness. ASME J. Appl. Mech. 57 (1990) 758-761. | Zbl
[12] and, On the optimization of fluid film bearings. Proc. Roy. Soc. London A 351 (1976) 481-497.
[13] , Regularity of solutions to a lubrication problem with discontinuous separation data. Nonlinear Anal. 53 (2003) 1167-1177. | Zbl
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