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Existence of solutions for elastohydrodynamic piezoviscous lubrication problems with a new model of cavitation

Published online by Cambridge University Press:  26 September 2008

G. Bayada ,
M. El Alaoui Talibi  and
C. Vázquez
G. Bayada
Affiliation:
CNRS URA 740–856. Math 403 I.N.S.A. 69621-Villeurbanne Cedex, France
M. El Alaoui Talibi
Affiliation:
Department of Mathematics. Fac. Sciences Semlalia. 40000-Marrakech, Morocco
C. Vázquez
Affiliation:
Department of Applied Mathematics. E.T.S.I. of Telecomunications. 36280-Vigo, Spain
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Abstract

The purpose of this paper 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 New Elrod–Adams model. This model introduces the concentration of fluid as well as the pressure as unknown functions and is suggested in preference to the classical variational inequality due to its ability to describe inflow and outflow. This leads to a nonlinear variational and nonlocal equation. Herein, an existence theorem is proved by means of two different techniques.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 7 , Issue 1 , February 1996 , pp. 63 - 73
Copyright
Copyright © Cambridge University Press 1996

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