Homogenization and two-scale convergence of the compressible Reynolds lubrication equation modelling the flying characteristics of a rough magnetic head over a rough rigid-disk surface

M. Jai

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1995)

  • Volume: 29, Issue: 2, page 199-233
  • ISSN: 0764-583X

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Jai, M.. "Homogenization and two-scale convergence of the compressible Reynolds lubrication equation modelling the flying characteristics of a rough magnetic head over a rough rigid-disk surface." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 29.2 (1995): 199-233. <http://eudml.org/doc/193772>.

@article{Jai1995,
author = {Jai, M.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {rapidly oscillating coefficients; slip flow; double-scale convergence; existence; uniqueness; limit solutions},
language = {eng},
number = {2},
pages = {199-233},
publisher = {Dunod},
title = {Homogenization and two-scale convergence of the compressible Reynolds lubrication equation modelling the flying characteristics of a rough magnetic head over a rough rigid-disk surface},
url = {http://eudml.org/doc/193772},
volume = {29},
year = {1995},
}

TY - JOUR
AU - Jai, M.
TI - Homogenization and two-scale convergence of the compressible Reynolds lubrication equation modelling the flying characteristics of a rough magnetic head over a rough rigid-disk surface
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1995
PB - Dunod
VL - 29
IS - 2
SP - 199
EP - 233
LA - eng
KW - rapidly oscillating coefficients; slip flow; double-scale convergence; existence; uniqueness; limit solutions
UR - http://eudml.org/doc/193772
ER -

References

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  2. [2] G. BAYADA and J. B. FAURE, 1989, A double scale analysis approach of the Reynolds roughness comments and application to the journal bearing, ASME, Journal of Tribology, 111. 
  3. [3] H. BREZIS, 1983, Analyse fonctionnelle. Théorie et applications, Masson, Paris. Zbl0511.46001MR697382
  4. [4] R. K. BRUNNER, J. M. HARKER, 1959, A gas film lubrication study. Part III : Experimental investigation of pivoted slider bearings, IBM Journal of Researchand Development, 8, 260-274. Zbl0108.39401MR105950
  5. [5] A. BURGDORFER, 1959, The influence of the molecular mean free path on the performance of hydrodynamic gas lubricated bearings, ASME Journal of Basic Engineering, 81, 99-100. 
  6. [6] M. CHIPOT and M. LUSKIN, 1986, Existence and uniqueness of solutions to the compressible Reynolds lubrication equation, Siam. J. Math. Anal., 17, 1390-1399. Zbl0645.76084MR860921
  7. [7] M. CHIPOT and J. CARILLO, 1985, On some nonlinear elliptic equations involving derivatives of the nonlinearity, Proc. Roy. Soc. Edinburgh, 100A, 281-294. Zbl0586.35044MR807707
  8. [8] H. CHRISTENSEN and K. TONDER, 1969, Tribology of rough surfaces : Stochastic models of hydrodynamic lubrication, SINTEF Report No 10/69-18. 
  9. [9] R. M. CRONE, M. S. JHON, B. BHUSHAN and T. E. KARIS, 1991, Modeling the flying characteristics of a rough magnetic head over a rough rigid-disk surface, ASME Journal of Tribology, 113, 4, 739-749. 
  10. [10] G. DUVAUT and M. ARTOLA, 1982, Un résultat d'homogénéisation pour une classe de problèmes de diffusion non linéaires stationnaires, Annales Faculté des Sciences, Toulouse, 4, 1-7. Zbl0517.35046MR673637
  11. [11] C. GREENGARD, 1989, Large bearing numbers and stationary Reynolds roughness, ASME Journal of Tribology, 111, 1, 136-141. 
  12. [12] M. JAI, 1991, A mixed finite difference method for diffusion convection problems. Application to singular perturbation problems, Equipe d'A.N. Lyon St-Etienne, N° 118. 
  13. [13] Y. MITSUYA, T. OHKUTO and H. OTA, 1989, Averaged Reynolds equation extended to gas lubricant possessing surface roughness in the slip flow regime : Approximate method and confirmation experiments, ASME Journal of Tribology, 111, 3, 495-503. 
  14. [14] G. NGUETSENG, 1989, A general convergence result for a functional related to the theory of homogenization, S.I.A.M. J. Math. Anal., 20, (3), 780-797. Zbl0688.35007MR990867
  15. [15] P. RAAD and J. W. WHITE, 1989, Entrance and stationary roughness effects on the load carrying capacity of a wide wedge gas bearing, ASME Journal of Tribology, 111, 1, 41-48. 
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  18. [18] J. WHITE, 1983, The effect of two sided surface roughness on ultra-thin gas films, ASME Journal of Tribology, 105, 3, 131-137. 

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