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Existence and Asymptotic Behavior of Global Solutions for a Class of Nonlinear Higher-Order Wave Equation

The initial boundary value problem for a class of nonlinear higher-order wave equation with damping and source term in a bounded domain is studied, where , is a nature number, and and are real numbers. The existence of global solutions for this problem is proved by constructing the stable sets and shows the asymptotic stability of the global solutions as time goes to infinity by applying the multiplier method.