Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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On the upper semicontinuity of pullback attractors for multi-valued processes


Author: Yejuan Wang
Journal: Quart. Appl. Math. 71 (2013), 369-399
MSC (2010): Primary 34K26, 35K55
DOI: https://doi.org/10.1090/S0033-569X-2013-01306-1
Published electronically: February 6, 2013
MathSciNet review: 3087428
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Abstract: This paper is concerned with the asymptotical behavior of multi-valued processes. First, we establish some stability results of pullback attractors for multi-valued processes and display new methods to check the continuity condition. Then we consider the effects of small time delays on the asymptotic stability of multi-valued nonautonomous functional parabolic equations. Finally, we give some new estimates of solutions and prove the existence of minimal pullback attractors in $ H_0^1(\Omega )$ for nonautonomous nonclassical diffusion equations with polynomial growth nonlinearity of arbitrary order and without the uniqueness of solutions. In particular, the upper semicontinuity of pullback attractors for nonclassical diffusion equations with singular and nonautonomous perturbations is addressed.


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Additional Information

Yejuan Wang
Affiliation: School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, People’s Republic of China
Email: wangyj@lzu.edu.cn

DOI: https://doi.org/10.1090/S0033-569X-2013-01306-1
Keywords: Multi-valued process, pullback attractor, parabolic equation with delay, small delay perturbation, nonclassical diffusion equation, singular point
Received by editor(s): August 21, 2011
Published electronically: February 6, 2013
Additional Notes: This research was supported by the National Natural Science Foundation of China under Grant No. 10801066 and by the Fundamental Research Funds for the Central Universities under Grant No. lzujbky-2011-47 and No. lzujbky-2012-k26
Article copyright: © Copyright 2013 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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