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Keywords:
nonlinear higher-order hyperbolic equation; nonlinear source term; global existence
nonlinear higher-order hyperbolic equation; nonlinear source term; global existence
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.
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