The aim of this work is to deduce the existence of solution
of a coupled problem arising in elastohydrodynamic
lubrication. The lubricant pressure and concentration are
modelled by Reynolds equation, jointly with the free-boundary
Elrod-Adams model in order to take into account cavitation
phenomena. The bearing deformation is solution of Koiter
model for thin shells. The existence of solution to the
variational problem presents some difficulties: the coupled
character of the equations, the nonlinear multivalued
operator associated to cavitation and the fact of writing the
elastic and hydrodynamic equations on two different domains.
In a first step, we regularize the Heaviside operator.
Additional difficulty related to the different
domains is circumvented by means of prolongation and
restriction operators, arriving to a regularized coupled
problem. This one is decoupled into elastic and hydrodynamic
parts, and we prove the existence of a fixed point for the
global operator. Estimations obtained for the
regularized problem allow us to prove the existence of
solution to the original one. Finally, a numerical method is proposed in order
to simulate a real journal-bearing device and illustrate the qualitative and
quantitative properties of the solution.