Asymptotic analysis for the elasticity system with Tresca and maximal monotone graph conditions

Abstract

In this paper, we consider the stationary problem in three dimensional thin domain \(\Omega ^{\varepsilon }\) with maximal monotone graph and Tresca conditions. In the first step, we present the problem statement and give the variational formulation. We then study the asymptotic behavior when one dimension of the domain tends to zero. In the latter case a specific Reynolds limit equation is obtained and the uniqueness of the displacement of the limit problem are proved.