Existence and numerical results of a transient lubrication problem with cavitation

This work is devoted to an existence result of a transient lubrication problem with a time dependent velocity and in the presence of cavitation which is modeled by the Elrod–Adams method. The existence of a solution is based on the time semi-discretization method which yields to a sequence of a second kind variational inequalities. We also give some numerical results for a journal bearing system.