Study of a dynamic viscoelastic problems with short memory

his paper is devoted to the study of the asymptotic behavior of a viscoelastic problem with short memory in a three-dimensional thin domain  $\Omega^\varepsilon$. We prove some convergence results when the thickness tends to zero. The contact is modeled with the Tresca friction law. We derive a variational formulation of the problem and prove its unique weak solution. Then we prove some convergence results when the small parameter $\varepsilon$ tends to zero. Finally, the specific Reynolds limit equation and the limit of Tresca-free boundary conditions are obtained.