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

Ionel Ciuperca; Mohamed El Alaoui Talibi; Mohammed Jai

ESAIM: Control, Optimisation and Calculus of Variations (2005)

- Volume: 11, Issue: 1, page 102-121
- ISSN: 1292-8119

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topCiuperca, Ionel, El Alaoui Talibi, Mohamed, and 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 11.1 (2005): 102-121. <http://eudml.org/doc/244634>.

@article{Ciuperca2005,

abstract = {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.},

author = {Ciuperca, Ionel, El Alaoui Talibi, Mohamed, Jai, Mohammed},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {compressible Reynolds lubrication equation; optimal control problems; Shauder fixed point theorem; quasilinear elliptic equation; coefficient control; necessary optimality conditions; existence of an optimal control},

language = {eng},

number = {1},

pages = {102-121},

publisher = {EDP-Sciences},

title = {On the optimal control of coefficients in elliptic problems. Application to the optimization of the head slider},

url = {http://eudml.org/doc/244634},

volume = {11},

year = {2005},

}

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

PB - EDP-Sciences

VL - 11

IS - 1

SP - 102

EP - 121

AB - 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.

LA - eng

KW - compressible Reynolds lubrication equation; optimal control problems; Shauder fixed point theorem; quasilinear elliptic equation; coefficient control; necessary optimality conditions; existence of an optimal control

UR - http://eudml.org/doc/244634

ER -

## References

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- [9] D. Kinderlehrer and G. Stampacchia, An introduction to variational inequalities and their applications. Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York (1980). Zbl0457.35001MR567696
- [10] L. Rayleigh, Notes on the Theory of Lubrication. Phylosophical Magazine 35 (1918) 1–12.
- [11] M.P. Robert, Optimization of self-acting gas bearings for maximum static siffness. ASME J. Appl. Mech. 57 (1990) 758–761. Zbl0718.76080
- [12] S.M. Rodhe and G.T. McAllister, On the optimization of fluid film bearings. Proc. Roy. Soc. London A 351 (1976) 481–497.
- [13] J. I. Tello, Regularity of solutions to a lubrication problem with discontinuous separation data. Nonlinear Anal. 53 (2003) 1167–1177. Zbl1126.76318

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