A 3D-2D asymptotic analysis of viscoelastic problem with nonlinear dissipative and source terms

摘要

The purpose of this article is to study the asymptotic analysis of the solutions of a linear viscoelastic problem with a dissipative and source terms in a three-dimensional thin domain omega(epsilon). Firstly, we give the strong formulation of the problem and the existence and uniqueness theorem of the weak solution. Then, we establish some estimates independent of the parameter epsilon. These last will be useful to obtain the limit problem with a specific weak form of the Reynolds equation.