Document Type : Research Paper

Authors

• Mustafa Derguine
• Abdelkader Saadallah
• Hamid Benseridi

Applied Mathematical Laboratory (lama), Faculty of Sciences, University of Setif 1 El Bez Setif 19000, Algeria

Abstract

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