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

Abstract

In this paper an inverse problem is considered for a non-coercive partial differential equation, issued from a mass conservation cavitation model for a slightly compressible fluid. 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.