Homogenization of the Stokes system in a thin film flow with rapidly varying thickness
Bayada, Guy ; Chambat, Michèle
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 23 (1989), p. 205-234 / Harvested from Numdam
@article{M2AN_1989__23_2_205_0,
     author = {Bayada, Guy and Chambat, Mich\`ele},
     title = {Homogenization of the Stokes system in a thin film flow with rapidly varying thickness},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {23},
     year = {1989},
     pages = {205-234},
     mrnumber = {1001328},
     zbl = {0675.76033},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1989__23_2_205_0}
}
Bayada, Guy; Chambat, Michèle. Homogenization of the Stokes system in a thin film flow with rapidly varying thickness. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 23 (1989) pp. 205-234. http://gdmltest.u-ga.fr/item/M2AN_1989__23_2_205_0/

[1] G. Bayada et M. Chambat, The transition between the Stokes equations and the Reynolds equation: a mathematical proof, Appl. Math. Opt. 14 (1986)73-93. | MR 826853 | Zbl 0701.76039

[2] G. Bayada et M. Chambat, On the various aspects of the thin film equation in hydrodynamic lubrification when the roughness occurs, in « Applications of multiple scaling in mechanics », Masson, Paris 1987. | MR 901987 | Zbl 0649.76013

[3] M. Chambart, G. Bayada et J. B. Faure, Some effects of the boundary roughness in a thin film flow, in « Boundary variation and boundary control », Proc. IFIP Conf. Nice, 1986, Lect. Notes Control Inf. Sciences, 100, Springer Verlag, Berlin 1988. | MR 942450 | Zbl 0651.76013

[4] G. Bayada et J. B. Faure, Application des techniques d'homogénéisation à des phénomènes de rugosité en lubrification hydrodynamique, Publications U.A. 740 CNRS Lyon St Etienne, 32 (1984) 1-52.

[5] A. Bensoussan, J. L. Lions et G. Papanicolaou, Asymptotic analysis for periodic structure, North Holland, Amsterdam 1978. | MR 503330 | Zbl 0404.35001

[6] D. Caillerie, Homogénéisation des équations de la diffusion stationnaire dans des domaines cylindriques aplatis, RAIRO Anal. Num.,15 (4) (1981) 295-319. | Numdam | MR 642495 | Zbl 0483.35003

[7] D. Caillerie, Thin Elastic and Periodic Plates, Math. Meth. in the Appl. Sci., 6 (1984) 159-191. | MR 751739 | Zbl 0543.73073

[8] K. K. Chen et D. C. Sun, On the statistical treatment of rough surface in hydrodynamic lubrication problems, Proc. of the 4th Leeds-Lyon Symp. on surface roughness in lubrication, IME (1977) 41-45.

[9] H. Christensen et K. Tonder, The hydrodynamic lubrication of rough bearing surfaces of finite width, J. of Lub. Tech., Trans. ASME, F, 93 (3) (1971) 324-330.

[10] V. Girault et P. A. Raviart, Finite element approximation of the Navier-Stokes equations, Springer Verlag, Berlin, 1981. | MR 548867 | Zbl 0441.65081

[11] R. Kohn et M. Vogelius, A new model for thin plates with rapidly varying thickness, Int. J. Solid and Struct., 20 (1984) 333-350. | Zbl 0532.73055

[12] R. Kohn et M. Vogelius, A new model for thin plates with rapidly varying thickness II. a convergence proof, Quart. of Appl Math. 18 (1985) 1-22. | MR 782253 | Zbl 0565.73046

[13] J. L. Lions, Perturbations singulières dans les problèmes aux limites en contrôle optimal, Springer Verlag, Berlin, 1973. | MR 600331 | Zbl 0268.49001

[14] N. Patir et H. S Cheng, An average flow model for determining effects of three dimensional roughness in partial hydrodynamic roughness, J of Lub. Tech., Trans. ASME, F 100 (1978) 12-17.

[15] N. Phan Thien, On the effects of the Reynolds and Stokes roughness in a two dimensional slider hearing, Proc. R. Soc. London, A377 (1981) 349-362. | Zbl 0481.76045

[16] N. Phan Thien, Hydrodynamic lubrication of rough surfaces, Proc. R. Soc. London, A383 (1982) 439-446. | Zbl 0535.76043

[17] J. Saint Jean Paulin, Homogénéisation et perturbations dans un problème lié à l'échauffement d'un câble électrique, Ann Fac. Sc., Toulouse 5 (1983) 43-59. | Numdam | MR 709810 | Zbl 0531.35010

[18] E. Sanchez-Palencia, Non homogeneous media and vibration theory, Lecture Notes in Physics 127, Springer Verlag, Berlin, 1978. | MR 578345 | Zbl 0432.70002

[19] D. C. Sun and K. K Chen, First effects of Stokes roughness on hydrodynamic lubrication, J. of Lub Tech., Trans. ASME, F, 99 (1977) 2-5.

[20] L. Tartar, Cours Peccot, Collège de France, 1977.

[21] J. L. Teale et A. O. Lebeck, An évaluation of the average flow model for surface roughness effects in lubrication, J. of Lub. Tech., Trans. ASME, F, 102 (1980) 360-367.

[22] R. Temam, Navier Stokes equation, North Holland, Amsterdam, 1979.