Paper Title
Variational and Convergence Asymptotic of a Dynamic Viscoelastic Problems

The aim of this paper is to study of the asymptotic behavior of non linear problem in a dynamic regime in a bounded domain of with nonlinear friction of Tresca type. In the first step, we derive a variational formulation of the mechanical problem. The existence and uniqueness of weak solution is proved prove. We study the limit when the tends to zero, we prove the convergence of the unknowns which are the displacement and the velocity and we obtain the limit problem and the specific Reynolds equation. Keywords - Asymptotic approach, Displacement field, Reynolds equation, Short memory, Treska law.