An elastohydrodynamic coupled problem between a piezoviscous Reynolds equation and a hinged plate model
Durany, J. ; García, G. ; Vásquez, C.
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 31 (1997), p. 495-516 / Harvested from Numdam
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@article{M2AN_1997__31_4_495_0,
     author = {Durany, J. and Garc\'\i a, G. and V\'asquez, C.},
     title = {An elastohydrodynamic coupled problem between a piezoviscous Reynolds equation and a hinged plate model},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {31},
     year = {1997},
     pages = {495-516},
     mrnumber = {1457458},
     zbl = {0879.73044},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1997__31_4_495_0}
}

Durany, J.; García, G.; Vásquez, C. An elastohydrodynamic coupled problem between a piezoviscous Reynolds equation and a hinged plate model. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 31 (1997) pp. 495-516. http://gdmltest.u-ga.fr/item/M2AN_1997__31_4_495_0/

[1] R. A. Adams, 1975, Sobolev Spaces. Academic Press. | MR 450957 | Zbl 0314.46030

[2] S. Alvarez, 1986, Problemas de Frontera Libre en Teoría de Lubrificatión.Thesis, University Complutense of Madrid, Spain.

[3] S. Balasundaram and P. K. Bhattacharyya, 1982, A mixed finite element method for the Dirichlet problem of fourth order elliptic operators with variable coefficients. In : Finite Element Methods in Flow Problems (Ed. T. Kawai) Tokyo Univ. Press. | Zbl 0508.76006

[4] G. Bayada, M. Chambat, 1984, Existence and uniqueness for a lubrication problem with nonregular conditions on the free boundary. Boll. UMI. 6, 3B, 543-557. | MR 762718 | Zbl 0612.35026

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

[6] G. Bayada, M. Chambat, 1986, Sur quelques modélisations de la zone de cavitation en lubrification hydrodynamique. J. of Theor. and Appl. Mech., 5, 703-729. | MR 878123 | Zbl 0621.76030

[7] G. Bayada, J. Durany, C. Vazquez, 1995, Existence of solution for a lubrication problem in elastic journal bearing devices with thin bearing. Math. Meth. in the Appl. Sc., 18, 255-266. | MR 1319998 | Zbl 0820.35110

[8] G. Bayada, M. El Alaoui, C. Vázquez, 1996, Existence of solution for elastohydrodynamic piezoviscous lubrication problems with a new model of cavitation. Eur. J. of Appl. Math., 7, 63-73. | MR 1381799 | Zbl 0856.76013

[9] A. Bermúdez, J. Durany, 1989, Numerical solution of cavitation problems in lubrication. Comp. Meth. in Appl. Mech. and Eng., 75, 457-466. | MR 1035758 | Zbl 0687.76030

[10] A. Bermúdez, C. Moreno, 1981, Duality methods for solving variational inequalities. Comp. Math, with Appl., 7, 43-58. | MR 593554 | Zbl 0456.65036

[11] A. Cameron, 1981, Basic Lubrication Theory. Ellis Horwood.

[12] M. Chipot, 1984, Variational Inequalities and Flow on Porous Media. Appl. Math. Sc. Series 52. Springer-Verlag. | MR 747637 | Zbl 0544.76095

[13] P. Ciarlet, 1978, The Finite Element Method for Elliptic Problems. North-Holland. | MR 520174 | Zbl 0383.65058

[14] P. Ciarlet, P. A. Raviart, 1974, A mixed finite element method for the biharmonic equation. In : Mathematical Aspects of Finite Elements in Partial Differential Equations. (Ed. C. de Boor), Academic Press, 125-145. | MR 657977 | Zbl 0337.65058

[15] G. Cimatti, 1983, How the Reynolds equation is related to the Stokes equation. Appl. Math. Opt., 10, 223-248. | MR 722490 | Zbl 0538.76038

[16] G. Cimatti, 1986, Existence and uniqueness for nonlinear Reynolds equations.Int. J. Eng. Sc. 24, N.5, 827-834. | MR 841923 | Zbl 0624.76090

[17] D. Dowson, C. M. Taylor, 1979, Cavitation in bearings. Ann. Rev. Fluid Mech.,35-66.

[18] J. Durany, G. Garcia, C. Vazquez, 1996, A mixed Dirichlet-Neumann problem for a nonlinear Reynolds equation in elastohydrodynamic piezoviscous lubncation. Proc. of the Edinb. Math Soc., 39, 151-162. | MR 1375675 | Zbl 0857.35044

[19] J. Durany, G García, C. Vázquez, 1996, Numerical computation of free boundary problems in elastohydrodynamic lubrication Appl. Math. Mod, 20, 104-113. | Zbl 0851.73058

[20] J. Durany, C. Vazquez, 1994, Mathematical analysis of an elastohydrodynamic lubrication problem with cavitation Appl. Anal. Vol. 53, N. 1, 135-142. | MR 1379190 | Zbl 0841.35133

[21] V. Glrault, P. A. Raviart, 1979, Finite Element Approximation of the Navier-Stokes Equations. Lecture Notes in Mathematics, 749, Springer. | MR 548867 | Zbl 0413.65081

[22] R. Glowinski, O. Pironneau, 1979, Numerical methods for the first biharmonic equation and for the two-dimensional Stokes problem SIAM Review, 21, 167-212. | MR 524511 | Zbl 0427.65073

[23] D. Kinderlehrer, G. Stampacchia, 1980, An Introduction to Variational Inequalities and their Applications Academic Press. | MR 567696 | Zbl 0457.35001

[24] O. Reynolds, 1986, On the theory of lubrication and its applications to M. Beauchamp Tower's experiments Phil. Trans. Roy. Soc. London, A117, 157-234. | JFM 18.0946.04