Asymptotic Study of a Boundary Value Problem Governed by the Elasticity Operator with Nonlinear Term

Abstract

In this paper, a nonlinear boundary value problem in a three dimensional thin domain with Tresca's friction law is considered. The small change of variable z = x₃/ε transforms the initial problem posed in the domain Ω^ε into a new problem posed on a fixed domain Ω independent of the parameter ε. As a main result, we obtain some estimates independent of the small parameter. The passage to the limit on ε, permits to prove the results concerning the limit of the weak problem and its uniqueness.