Criteria on the existence and stability of pullback exponential attractors and their application to non-autonomous kirchhoff wave models

Zhijian Yang; Yanan Li

doi:10.3934/dcds.2018111

Article Contents

2018, Volume 38, Issue 5: 2629-2653. Doi: 10.3934/dcds.2018111

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Criteria on the existence and stability of pullback exponential attractors and their application to non-autonomous kirchhoff wave models

Zhijian Yang^, and
Yanan Li

School of Mathematics and Statistics, Zhengzhou University, No.100, Science Road, Zhengzhou 450001, China

* Corresponding author: Zhijian Yang
* Corresponding author: Zhijian Yang

Received: April 30, 2017

Revised: October 31, 2017

Published: June 2018

This work is supported by National Natural Science Foundation of China (No.11671367)

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Abstract

In this paper, we are concerned with the existence and stability of pullback exponential attractors for a non-autonomous dynamical system. (ⅰ) We propose two new criteria for the discrete dynamical system and continuous one, respectively. (ⅱ) By applying the criteria to the non-autonomous Kirchhoff wave models with structural damping and supercritical nonlinearity we construct a family of pullback exponential attractors which are stable with respect to perturbations.

Keywords:

Pullback exponential attractor,
stability with respect to perturbations,
non-autonomous Kirchhoff wave equations,
structural damping,
supercritical nonlinearity.

Mathematics Subject Classification: Primary: 37L15, 37L30; Secondary: 35B40, 35B41.

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