Differential and Integral Equations

A note on some inverse problems arising in lubrication theory

J. I. Díaz and J. I. Tello

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It is well-known that the pressure of a lubricating fluid filling the gap between two solid surfaces satisfies the Reynolds equation involving the distance function, $h$, between both planes, as a crucial coefficient. Nevertheless, in most of the applications the function $h$ is not known a priori. Here we consider the simple case in which the surfaces are two parallel planes and assume prescribed the total force applied upon one of the surfaces. We give some sufficient conditions on the total force in order to solve this inverse problem. We show that in the incompressible case, such a condition is also necessary.

Article information

Differential Integral Equations, Volume 17, Number 5-6 (2004), 583-591.

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35R30: Inverse problems
Secondary: 35Q35: PDEs in connection with fluid mechanics 76D08: Lubrication theory


Díaz, J. I.; Tello, J. I. A note on some inverse problems arising in lubrication theory. Differential Integral Equations 17 (2004), no. 5-6, 583--591. https://projecteuclid.org/euclid.die/1356060349

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