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

Tingting Liu; Qiaozhen Ma

doi:10.3934/dcdsb.2018178

Article Contents

2018, Volume 23, Issue 10: 4595-4616. Doi: 10.3934/dcdsb.2018178

This issue Previous Article Prevalence of stable periodic solutions in the forced relativistic pendulum equation Next Article

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

Tingting Liu and
Qiaozhen Ma^,

School of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

* Corresponding author
* Corresponding author

Received: August 31, 2017

Revised: December 31, 2017

Early access: May 2018

Published: September 2018

Ma is supported by NSF grant(11561064, 11361053), and partly supported by NWNU-LKQN-14-6.

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Abstract

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.

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

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