About an inverse problem for a free boundary compressible problem in hydrodynamic lubrication

In this paper an inverse problem is considered for a non coercive partial di erential equation, issued from a mass conservation cavitation model for a slightly compressible uid. The cavitation phenomenon and compressibility take place and are described by the Elrod model. The existence of an optimal solution is proven. Optimality conditions are derived and some numerical results are given.