Asymptotic behavior of a viscoelastic problem with long-term memory and Tresca friction law

This paper examines the asymptotic behavior of solutions of the three dimensional viscoelastic problem with long-term memory and Tresca friction law in a thin domain Σε. We study the asymptotic behavior of this problem when the thickness ε tends to zero and we prove a convergence theorem for the displacement and velocity in appropriate functional spaces. Besides, the limit problem with the limit of Tresca free boundary conditions and a specific Reynolds limit equation is obtained.