## Differential and Integral Equations

### A note on some inverse problems arising in lubrication theory

#### Abstract

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

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

Dates
First available in Project Euclid: 21 December 2012

https://projecteuclid.org/euclid.die/1356060349

Mathematical Reviews number (MathSciNet)
MR2054936

Zentralblatt MATH identifier
1224.35335

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

#### Citation

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