Existence of a solution for a lubrication problem in elastic journal- bearing devices with thin bearing. (English) Zbl 0820.35110

Summary: A particular elastohydrodynamic lubrication problem is modelled in this work. The presence of elasticity, lubrication and cavitation calls for a nonlinear coupled system of variational equations. The existence of a solution is deduced by means of a constructive algorithm that decouples the biharmonic equation of the elastic hinged plate and the lubrication- cavitation Elrod-Adams free boundary problem.


35Q35 PDEs in connection with fluid mechanics
76D08 Lubrication theory
35J60 Nonlinear elliptic equations
35R35 Free boundary problems for PDEs
Full Text: DOI


[1] ’Problemas de Frontera Libre en Teoría de Lubrificación’, Ph.D. Thesis, University Complutense of Madrid, Spain, 1986.
[2] Bayada, Appl. Math. Optim. 14 pp 73– (1986)
[3] Bayada, Jour. Mec. Th. Appl. 5 pp 703– (1986)
[4] Brezis, C.R. Acad. Sci. Paris. 187 pp 711– (1978)
[5] Cimatti, Appl. Math. Optim. 10 pp 223– (1983)
[6] Cimatti, Int. J. Eng. Sci. 24 pp 827– (1986)
[7] and , Elastohydrodynamic Lubrication, Pergamon, Oxford, 1966.
[8] and , An Introduction to Variational Inequalities and Their Applications, Academic Press, New York, 1980.
[9] Perturbations Singulieres dans les Problémes aux Limites et en Controle Optimal, Lecture Notes in Mathematics, Vol. 323, Springer, Berlin, 1973. · doi:10.1007/BFb0060528
[10] Oden, Int. J. Eng. Sci. 23 pp 207– (1985)
[11] Variational Methods in Mathematics Science and Engineering, Reidel, Dordrecht, Publishing Company 1977. · doi:10.1007/978-94-011-6450-4
[12] Reynolds, Phil. Trans. Roy. Soc. London A117 pp 157– (1886)
[13] Savage, J. Fluid Mech. 80 pp 734– (1977)
[14] ’Análisis matemático y resolución numérica de problemas de lubricatión con cavitación’, Ph.D. Thesis, University of Santiago, Spain, 1992.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.