zbMATH — the first resource for mathematics

Existence of solutions for elastohydrodynamic piezoviscous lubrication problems with a new model of cavitation. (English) Zbl 0856.76013
Summary: The purpose is to study a mathematical model of lubricating flow between elastic surfaces obeying the linear Hertzian theory when cavitation takes place. Cavitation is a free boundary phenomenon that is described in this paper by the Elrod-Adams model. This model introduces the concentration of fluid as well as the pressure as unknown functions; we suggest the model in preference to the classical variational inequality due to its ability to describe inflow and outflow. This leads to a nonlinear variational nonlocal equation. Herein, an existence theorem is proved by means of two different techniques.

76D08 Lubrication theory
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
Full Text: DOI
[1] Goeleven, Bull. Australian Math. Soc. 50 pp 353– (1994)
[2] Bayada, J. Theor. Appl. Mech. 5 pp 703– (1986)
[3] DOI: 10.1137/0521002 · Zbl 0718.35101 · doi:10.1137/0521002
[4] DOI: 10.1016/0020-7225(85)90075-8 · doi:10.1016/0020-7225(85)90075-8
[5] V?zquez, Adv. in Math. Sci. and Appl. 4 pp 313– (1994)
[6] DOI: 10.1088/0022-3727/5/12/309 · doi:10.1088/0022-3727/5/12/309
[7] Brezis, C.R. Acad. Sci. 187 pp 711– (1978)
[8] Gilbarg, Elliptic partial Differential Equations of Second Order (1977) · doi:10.1007/978-3-642-96379-7
[9] Chipot, Variational Inequalities and Flow on Porous Media (1984) · doi:10.1007/978-1-4612-1120-4
[10] Bissett, Proc. R. Soc. A424 pp 393– (1989) · Zbl 0674.73079 · doi:10.1098/rspa.1989.0091
[11] Kinderlehrer, An Introduction to Variational Inequalities and their Applications (1980) · Zbl 0457.35001
[12] Elliott, Weak and Variational Methods for Moving Boundary Problems (1982) · Zbl 0476.35080
[13] DOI: 10.1146/annurev.fl.11.010179.000343 · doi:10.1146/annurev.fl.11.010179.000343
[14] Bayada, Boll. U.M.I. 6 pp 543– (1984)
[15] Rodr?gues, Euro. J. Appl. Math. 4 pp 83– (1993)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.