Existence and Uniqueness Result for a Perturbed Purely Elastodynamic Problem with Friction

We consider the dynamic process of an elastic body submitted to unilateral contact and friction with a rigid foundation. Friction is modelized with a Coulomb law with a coefficient possibly depending on the slip velocity. To keep a possibility of velocity discontinuities we use the elastodynamic (hyperbolic) framework. Nevertheless, this does not allow to get a well-posed problem. To make up for this, we perturb the solution of the elastodynamic problem in a thin layer next to the contact boundary. This is a generalization of an approach precedently studied in a one-dimensional case. We establish existence and uniqueness results for this perturbed problem and give an interpretation of this perturbation