Uniform attractors for non-autonomous plate equations with $ p $-Laplacian perturbation and critical nonlinearities

Xin-Guang Yang; Marcelo J. D. Nascimento; Maurício L. Pelicer

doi:10.3934/dcds.2020100

Article Contents

2020, Volume 40, Issue 3: 1937-1961. Doi: 10.3934/dcds.2020100

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Uniform attractors for non-autonomous plate equations with $ p $-Laplacian perturbation and critical nonlinearities

1.
College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China
2.
Departamento de Matemática, Universidade Federal de São Carlos, 13565-905 São Carlos SP, Brazil
3.
Departamento de Ciências, Campus Regional de Goioerê, Universidade Estadual de Maringá, 87360-000, Goioerê, PR, Brazil

^* Corresponding author: Marcelo J. D. Nascimento
^* Corresponding author: Marcelo J. D. Nascimento

Received: June 30, 2019

Revised: September 30, 2019

Published: December 2019

The first author is partially supported by the Key Project of Science and Technology of Henan Province (Grant No. 182102410069) and the Fund of Young Backbone Teacher in Henan Province (No. 2018GGJS039)
The second author is partially supported by FAPESP grant # 2017/06582-2, Brazil

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Abstract

This paper is concerned with the long-time behavior for a class of non-autonomous plate equations with perturbation and strong damping of $ p $-Laplacian type

$ u_{tt} + \Delta^2 u + a_{\epsilon}(t) u_t - \Delta_p u - \Delta u_t + f(u) = g(x,t), $

in bounded domain $ \Omega\subset \mathbb{R}^N $ with smooth boundary and critical nonlinear terms. The global existence of weak solution which generates a continuous process has been presented firstly, then the existence of strong and weak uniform attractors with non-compact external forces also derived. Moreover, the upper-semicontinuity of uniform attractors under small perturbations has also obtained by delicate estimate and contradiction argument.

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Mathematics Subject Classification: Primary: 35L75, 37B55; Secondary: 35B41, 74K20.

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