Pullback Attractors for a Non-Autonomous Plate System with Strong Damping and Delay

Abstract

This paper addresses the existence of pullback attractors for a class of nonlinear non-autonomous strongly damped plate equations with delay. The model contains the biharmonic operator, the strong damping term, a nonlinear source term and a delay operator acting on the history of the solution. The interaction between the strong damping mechanism and the hereditary delay effect gives rise to several analytical difficulties in deriving uniform estimates and proving pullback asymptotic compactness. To overcome these difficulties, we construct a modified energy functional adapted to the strong damping structure and employ the contractive function method to handle the delay term in the history phase space. By establishing the existence and uniqueness of weak solutions, uniform pullback estimates and the pullback asymptotic compactness of the associated non-autonomous process, we prove the existence of pullback attractors for the strongly damped plate equation with delay.

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BibTeX RIS

BibTeX

@misc{hou2026pullback,
  title = {{Pullback Attractors for a Non-Autonomous Plate System with Strong Damping and Delay}},
  author = {Xuxiao Hou and Bin Yang and Yuming Qin and Alain Miranville},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.15110},
  eprint = {2609.15110},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.15110},
}

RIS

TY  - UNPB
TI  - Pullback Attractors for a Non-Autonomous Plate System with Strong Damping and Delay
AU  - Xuxiao Hou
AU  - Bin Yang
AU  - Yuming Qin
AU  - Alain Miranville
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.15110
UR  - https://arxiv.org/abs/2609.15110
AB  - This paper addresses the existence of pullback attractors for a class of nonlinear non-autonomous strongly damped plate equations with delay. The model contains the biharmonic operator, the strong damping term, a nonlinear source term and a delay operator acting on the history of the solution. The interaction between the strong damping mechanism and the hereditary delay effect gives rise to several analytical difficulties in deriving uniform estimates and proving pullback asymptotic compactness. To overcome these difficulties, we construct a modified energy functional adapted to the strong damping structure and employ the contractive function method to handle the delay term in the history phase space. By establishing the existence and uniqueness of weak solutions, uniform pullback estimates and the pullback asymptotic compactness of the associated non-autonomous process, we prove the existence of pullback attractors for the strongly damped plate equation with delay.
ER  -

Abstract

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