Source term model for elasticity system with nonlinear dissipative term in a thin domain

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.

Keywords

• asymptotic behavior
• dissipative term
• source term
• tresca friction law
• weak solution
• 35r35
• 76f10
• 78m35
• 35b40
• 35j85
• 49j40