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 Faedo-Galarkin method. We also established the asymptotic behavior of global solutions as $t\rightarrow\infty$ by applying the Lyapunov method.

Keywords

• nonlinear higher-order hyperbolic equation
• nonlinear source term
• global existence