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

K. Ait Hadi (1) , Guy Bayada (2, 3) , M. El Alaoui Talibi (1)

1 LIBMA - Laboratoire Ibn Al-Banna de Mathématiques et Applications
2 ICJ - Institut Camille Jordan
3 MMCS - Modélisation mathématique, calcul scientifique

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.

Domaines: Modélisation et simulation; Mathématiques [math]; Optimisation et contrôle [math.OC]

K. Ait Hadi, Guy Bayada, M. El Alaoui Talibi. About an inverse problem for a free boundary compressible problem in hydrodynamic lubrication. Journal of Inverse and Ill-posed Problems, 2015. ⟨hal-00822388⟩