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

Mama Abdelli; Abderrahmane Beniani; Nadia Mezouar; Ahmed Chahtou — 2023

Mathematica Bohemica

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 $t \to \infty$ by applying the Lyapunov method.

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