Existence, uniqueness and homogenization for a class of second–order nonlinear equations with nonlinear boundary damping term in perforated domains

Abstract

In this paper, we study the existence, uniqueness and homogenization of a nonlinear hyperbolic problem with nonlinear boundary damping term [Formula: see text] and a boundary source term [Formula: see text] where [Formula: see text] At first, we prove the existence and uniqueness of a solution related to this problem through using the Faedo–Galerkin method. Besides, under certain assumptions on the problem’s coefficients and according to the oscillating test function method, we pass to the limit (when [Formula: see text]) and we get a nonlinear hyperbolic problem with zero Dirichlet boundary condition.