STUDY OF THE VISCOELASTIC PROBLEMS WITH SHORT MEMORY IN A THIN DOMAIN WITH TRESCA BOUNDARY CONDITIONS

Abstract

In this paper, we are interested in the study of the asymptotic behavior of non linear problem in a quasistatic regime in a thin domain with Tresca boundary conditions. In the first step, we derive a variational formulation of the mechanical problem and prove the existence and uniqueness of the weak solution. We study the limit when the ε 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.