Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 14 1 2023 01 01 Study of a dynamic viscoelastic problems with short memory 1911 1923 7180 10.22075/ijnaa.2022.27280.3547 EN Mustafa Derguine Applied Mathematical Laboratory (lama), Faculty of Sciences, University of Setif 1 El Bez Setif 19000, Algeria Abdelkader Saadallah Applied Mathematical Laboratory (lama), Faculty of Sciences, University of Setif 1 El Bez Setif 19000, Algeria Hamid Benseridi Applied Mathematical Laboratory (lama), Faculty of Sciences, University of Setif 1 El Bez Setif 19000, Algeria Journal Article 2022 05 24 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. https://ijnaa.semnan.ac.ir/article_7180_5efc35c64c378b91a0a1f04f4bfd546f.pdf