Existence and exponential decay estimates for a system of nonlinear wave equations with nonlinear boundary conditions

Abstract

The paper is devoted to the study of a system of nonlinear equations with nonlin- ear boundary conditions. First, based on Faedo-Galerkin method and standard arguments of density corresponding to the regularity of initial conditions, we establish two global existence theorems of weak solutions. Next, the exponential decay property of the global solution via the construction of a suitable Lyapunov functional is presented.