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.