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.

Keywords:

asymptotic approach , boundary value problem , displacement field , Reynolds equation , short memory