# 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 (2010)

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

## Access Full Article

top## Abstract

top## How to cite

topCiuperca, Ionel, Mohamed El Alaoui Talibi, 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 (2010): 102-121. <http://eudml.org/doc/90752>.

@article{Ciuperca2010,

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, Mohamed El Alaoui Talibi, 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},

month = {3},

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/90752},

volume = {11},

year = {2010},

}

TY - JOUR

AU - Ciuperca, Ionel

AU - Mohamed El Alaoui Talibi

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

DA - 2010/3//

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/90752

ER -

## References

top- A. Bensoussan, J.L. Lions and G. Papanicolaou, Asymptotic analysis for periodic structure. North-Holland (1978). Zbl0404.35001
- B. Burgdorfer, The influence of the molecular mean free path on the performance of hydrodynamic gas lubricated bearings. ASME J. basic Engineer.81 (1959) 99–100.
- M. Chipot and M. Luskin, Existence and uniqueness of solutions to the compressible Reynolds lubrication equation. SIAM J. Math. Anal.17 (1986) 1390–1399. Zbl0645.76084
- J.I. Diaz and J.I. Tello, On a problem lacking a classical solution in lubrication theory, in Actas del XV-CEDYA, VigoII (1997) 429–434. Zbl0934.35128
- L.C. Evans and R.F. Gariepy, Measure theory and fine properties of functions. Stud. Adv. Math. CRC Press (1992). Zbl0804.28001
- D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order. Springer-Verlag, Berlin, second edition (1983). Zbl0562.35001
- B.S. Grigor'ev, S.V. Lupulyak and Yu.K. Shinder, Solvability of the reynolds equation of gas lubrication. J. Math. Sci.106 (2001) 2925–2928.
- M. Jai, Existence and uniqueness of solutions of the parabolic nonlinear compressible Reynolds lubrication equation. Nonlinear Anal.43 (2001) 655–682. Zbl0964.35083
- D. Kinderlehrer and G. Stampacchia, An introduction to variational inequalities and their applications. Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York (1980). Zbl0457.35001
- L. Rayleigh, Notes on the Theory of Lubrication. Phylosophical Magazine35 (1918) 1–12.
- M.P. Robert, Optimization of self-acting gas bearings for maximum static siffness. ASME J. Appl. Mech.57 (1990) 758–761. Zbl0718.76080
- S.M. Rodhe and G.T. McAllister, On the optimization of fluid film bearings. Proc. Roy. Soc. London A 351 (1976) 481–497.
- J. I. Tello, Regularity of solutions to a lubrication problem with discontinuous separation data. Nonlinear Anal.53 (2003) 1167–1177. Zbl1126.76318

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.