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Time-dependent asymptotic behavior of the solution for plate equations with linear memory

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    * Corresponding author
Ma is supported by NSF grant(11561064, 11361053), and partly supported by NWNU-LKQN-14-6.
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  • In this article, we consider the long-time behavior of solutions for the plate equation with linear memory. Within the theory of process on time-dependent spaces, we investigate the existence of the time-dependent attractor by using the operator decomposition technique and compactness of translation theorem and more detailed estimates. Furthermore, the asymptotic structure of time-dependent attractor, which converges to the attractor of fourth order parabolic equation with memory, is proved. Besides, we obtain a further regular result.

    Mathematics Subject Classification: Primary: 35B40; 35K30; Secondary: 37B55; 35B25.

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