Asymptotic Analysis of a Dynamic Viscoelastic Problem with Short Memory

Abstract

This thesis investigates the asymptotic analysis of a dynamic viscoelastic problem with short memory in a thin domain under Tresca friction conditions. It first introduces the essential mathematical tools, including functional analysis and Sobolev spaces. The problem is then formulated in a variational framework, where a priori estimates and convergence results are established. Finally, the limit problem, the generalized Reynolds equation, and the uniqueness of the solution are derived and proved.