Behavior of the isothermal Elasticity operator with non-linear friction in a thin domain

Abstract

This paper deals with the asymptotic behavior of a boundary value problem in a three dimensional thin domain Ω ε with non-linear friction of Coulomb type. We will establish a variational formulation for the problem and prove the existence and uniqueness of the weak solution. We then study the asymptotic behavior when one dimension of the domain tends to zero. In which case, the uniqueness result of the displacement for the limit problem is also proved.