Existence and stability results of nonlinear higher-order wave equation with a nonlinear source term and a delay term

Abstract

We consider the initial-boundary value problem for a nonlinear higher-order nonlinear hyperbolic equation in a bounded domain. The existence of global weak solutions for this problem is established by using the potential well theory combined with FaedoGalarkin method. We also established the asymptotic behavior of global solutions as t → ∞ by applying the Lyapunov method.