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

Dilmi Mohamed, Dilmi Mourad, Boulaaras Salah, Benseridi Hamid

Demonstratio Mathematica

2022

Vol. 55, nr 1

437--451

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∗ 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.