On the asymptotic convergence of different boundary problems in a thin layer

Abstract

The object of the doctoral thesis is the study of the asymptotic behavior of some boundary problems modeling the behavior of fluids or of different materials in the dynamic and stationary case and this in a bounded domain in dimension three in thin film with the conditions of friction of Tresca. One of the goals of asymptotic analysis is to obtain an equation in dimension 3 of space (3D) which allows a reasonable description of the phenomenon occurring in a three-dimensional (3D) domain. This process is implemented by moving to the limit towards 0 over the thickness of the supposedly thin (3D) domain. In the first part of the thesis we will only consider viscoelastic anisotropic materials given by the linear behavior law Kelvin-Voigt, and in the second part it will be a question of seeing to what extent we can generalize the results to the nonlinear case of materials viscoelastic. We are also interested in this doctoral thesis in the asymptotic analysis of thermal flow in a thin film of an incompressible Non-Newtonian fluid whose viscosity depends on temperature. In this case, the mechanical problem leads to a coupled mathematical model, formed from the equation of motion and the equation of energy conservation