Asymptotic behavior of a nonlinear viscoelastic problems with Tresca friction law in a thin domain

In this paper, we consider a nonlinear mathematical model which describes the deformation of a viscous body in a three-dimensional thin domain with the presence of Tresca’s friction law. We examine the asymptotic behavior of the weak solutions when one dimension of the domain tends to zero. The two-dimensional limit problem has been justified. The uniqueness result of the displacement and the limit form of the Tresca boundary conditions are obtained.