Robustness of global attractors of singularly perturbed plate equations

Abstract

In the paper, upper semicontinuity of global attractors of singularly perturbed plate equations on an unbounded domain with small positive parameter is considered. Under suitable assumptions, the equations possess a family of global attractors in natural energy space, and the corresponding singular limit equation, i.e. the parabolic equation, possesses a global attractor, which can be naturally embedded into a compact set of the natural energy space, and the upper semicontinuity of the family of global attractors to the compact set in the natural energy space (even more regular space) with respect to the Hausdorff semidistance, as the perturbation parameter tends to zero, was proved.

Keywords:

• Upper semicontinuity
• singular perturbation
• plate equations
• global attractors
• Unbounded domain

2000 Mathematics Subject Classifications:

• 35B40
• 35L70
• 58F12
• 58G16

Acknowledgments

The author is greatly indebted to professor Xiao-biao Lin for his invitation to NCSU, where the work was completed.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Haibin Xiao http://orcid.org/0000-0001-7566-3624

Additional information

Funding

This work was supported by Natural Science Foundation of Zhejiang Province [grant number LY14A010004], China Scholarship Foundation [grant number 201208330224], and also sponsored by K.C.Wong Magna Fund in Ningbo University.