Source term model for elasticity system with nonlinear dissipative term in a thin domain
Mohamed Dilmi, Mourad Dilmi, Salah Boulaaras, Hamid Benseridi · Demonstratio Mathematica · 2022
Abstract This article establishes an asymptotic behavior for the elasticity systems with nonlinear source and dissipative terms in a three-dimensional thin domain, which generalizes some previous works. We consider the limit when the thickness tends to zero, and we prove that the limit solution u ∗ {u}^{\ast } is a solution of a two-dimensional boundary value problem with lower Tresca’s free-boundary conditions. Moreover, we obtain the weak Reynolds-type equation.