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Time-Dependent Global Attractors for Beam Equation with Time Delay and Structural Damping

DOI: 10.4236/jamp.2026.141008, PP. 139-165

Keywords: Delay, Structural Damping, Time-Dependent Global Attractors, Beam Equation

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Abstract:

In this article, the asymptotic behavior of the solutions to the beam equation with time delay and structural damping is considered. First of all, when the growth exponent of nonlinear terms satisfies the optimal growth exponent 1≤p< p * = N+2( 1+α ) N？4 , with N≥5 , the well-posedness of solutions is obtained by applying Faedo-Galerkin approximation method and time translation method; Then, the asymptotic compactness of the solution process is verified by using the contraction function method; Finally, the existence of time-dependent global attractor is established in the time-dependent space C ？ t 2 .

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