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

Abstract

top
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.

How to cite

top

Ciuperca, 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
  1. A. Bensoussan, J.L. Lions and G. Papanicolaou, Asymptotic analysis for periodic structure. North-Holland (1978).  Zbl0404.35001
  2. 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.  
  3. 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
  4. 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
  5. L.C. Evans and R.F. Gariepy, Measure theory and fine properties of functions. Stud. Adv. Math. CRC Press (1992).  Zbl0804.28001
  6. D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order. Springer-Verlag, Berlin, second edition (1983).  Zbl0562.35001
  7. 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.  
  8. M. Jai, Existence and uniqueness of solutions of the parabolic nonlinear compressible Reynolds lubrication equation. Nonlinear Anal.43 (2001) 655–682.  Zbl0964.35083
  9. D. Kinderlehrer and G. Stampacchia, An introduction to variational inequalities and their applications. Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York (1980).  Zbl0457.35001
  10. L. Rayleigh, Notes on the Theory of Lubrication. Phylosophical Magazine35 (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

NotesEmbed ?

top

You must be logged in to post comments.

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

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.