Mathematical analysis of an elastohy-drodynamic lubrication problem with cavitation

Abstract

In this work, a Second order non-linear elliptic boundary value problem with discontinuous coefficients arising in elastohydrodynamic lubrication is studied. Physically, it corresponds to a two dimensional model of the contact between an elastie rolling ball and a plane lubricated by a thin fluid film, when the viscosity is assumed to be constant. The model of Elrod-Adams is introduced in order to take into account the phenomenon of cavitation. A result of existence is obtained by means of regularization and fixed point techniques.