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

summary: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

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

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