EXISTENCE, BLOW-UP AND EXPONENTIAL DECAY ESTIMATES FOR A SYSTEM OF NONLINEAR VISCOELASTIC WAVE EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

摘要

This paper is devoted to the study of a system of nonlinear viscoelastic wave equations with nonlinear boundary conditions. Based on the Faedo-Galerkin method and standard arguments of density corresponding to the regularity of initial conditions, we first establish two local existence theorems of weak solutions. By the construction of a suitable Lyapunov functional, we next prove a blow up result and a decay result of global solutions.