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In this paper, we consider a non-linear problem in a stationary regime in a three-dimensional thin domain \(\Omega^{\varepsilon}\) with Fourier and Tresca boundary conditions. In the first step, we derive a variational formulation of the mechanical problem. We then study the asymptotic behavior in the one dimension case when the domain parameter tends to zero. In the latter case, a specific Reynolds equation associated with variational inequalities is obtained and the uniqueness of the limit velocity and pressure are proved.

Asymptotic behavior of solutions to a boundary value problem with mixed boundary conditions and friction law