Attractor of the Kirchhoff type plate equation with memory and nonlinear damping on the whole time-dependent space

Tingting Liu; Qiaozhen Ma; Ling Xu

doi:10.3934/dcdsb.2022046

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2022, Volume 27, Issue 12: 7351-7372. Doi: 10.3934/dcdsb.2022046

This issue Previous Article Coexisting singular cycles in a class of three-dimensional three-zone piecewise affine systems Next Article Synchronization of dynamical systems on Riemannian manifolds by an extended PID-type control theory: Numerical evaluation

Attractor of the Kirchhoff type plate equation with memory and nonlinear damping on the whole time-dependent space

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

^* Corresponding author
^* Corresponding author

Received: July 31, 2021

Revised: December 31, 2021

Early access: March 2022

Published: December 2022

Ma and Liu are supported by NSF grant(11961059, 12101502)

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Abstract

First of all, by virtue of the Faedo-Galerkin procedure, we obtain existence of solution for the Kirchhoff type plate equation with memory and nonlinear damping on $ \mathbb{R}^{n}. $ Secondly, using a new method of asymptotic contractive functions presented in [9] as well as the tail estimates we prove the asymptotic compactness of solution process. Finally, existence of the time-dependent attractor on $ \mathbb{R}^{n} $ is shown. The results are new and they are the extension and improvement of [9].

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Mathematics Subject Classification: Primary: 35B41, 37B55; Secondary: 45K05.

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