×

A free boundary problem in theory of lubrication. (English) Zbl 0809.35166

From the introduction: We study a problem related to the lubrication with cavitation arising in bearings. This problem was previously studied by G. Bayada and M. Chambat [Boll. Unione Mat. Ital., IV. Ser., B 3, 543-557 (1984; Zbl 0612.35026)]. They stated the problem and proved the existence of solutions; they proved uniqueness of solutions, under regularity assumptions on the free boundary.
The goal of this paper is to prove comparison and uniqueness of solutions without assuming condition related to the free boundary.

MSC:

35R35 Free boundary problems for PDEs
76D08 Lubrication theory
49J40 Variational inequalities

Citations:

Zbl 0612.35026
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Alvarez S.J, Problems de frontera libre en teoria de lubrification lubrication (1989)
[2] Qualitative properties of the free boundary of the Reynolds equation in lubrication 33 pp 235– (1989)
[3] Bayada G., Nonlinear variational formulation for a cavitation problem in lubricant, 90 pp 286– (1982) · Zbl 0502.76054
[4] Bayada G., Existence and uniquess for a lubrication problem with nonregular conditions on the free boundary, 6 (3) pp 543– (1984) · Zbl 0612.35026
[5] Bermudez A., Numerical solutions of cavitation problems in lubrication, 6 (3) (1989)
[6] Boukrouche M., Mathematical model. Existence and uniquess of cavitations problems in porous journal bearing 20 (8) pp 895– (1993) · Zbl 0773.35049
[7] Boukrouche M., The characteristics method to solve a stationary semi-coercive free boundary problemof hydrodynamic lubrication withcavitation and subject to an integral condition, · Zbl 0796.76030
[8] Brezis H., Sur une nouvelle formulation du problème de I’écoulemeni à travers une digue 287 pp 711– (1978)
[9] Carrillo J., Unicité des solutions pour une famille de problèmes ellip-tiques avec convection non linéaire (1985)
[10] Carrillo J., Unicité des solutions du type Kruskov pour des problèmes elliptiques avec des termes de transport non linéaires 303 (5) pp 189– (1986) · Zbl 0623.35030
[11] Carrillo J., On the uniqueness of the solution of the evolution dam problem 22 (5) pp 573– (1994) · Zbl 0810.76086
[12] Carrillo J., On some non linear elliptic equations involving derivatives of the nonlinearity 100 (5) pp 281– (1985) · Zbl 0586.35044
[13] Dowson D., Cavitation in bearings 11 (5) (1979)
[14] DOI: 10.1007/978-3-642-61798-0 · Zbl 0361.35003 · doi:10.1007/978-3-642-61798-0
[15] Shenq Guo Jong, A variational inequality associated with a lubrication problem 16 (1) pp 13– (1991) · Zbl 0732.35033
[16] Kinderlehrer D., An introduction to variational inequalities and their applications (1980) · Zbl 0457.35001
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.