Dynamics of strongly damped wave equations in locally uniform spaces: Attractors and asymptotic regularity

Authors:
Meihua Yang and Chunyou Sun

Journal:
Trans. Amer. Math. Soc. **361** (2009), 1069-1101

MSC (2000):
Primary 37L05, 35B40, 35B41

Published electronically:
September 29, 2008

MathSciNet review:
2452835

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Abstract: This paper is dedicated to analyzing the dynamical behavior of strongly damped wave equations with critical nonlinearity in locally uniform spaces. After proving the global well-posedness, we first establish the asymptotic regularity of the solutions which appears to be optimal and the existence of a bounded (in ) subset which attracts exponentially every initial -bounded set with respect to the -norm. Then, we show there is a -global attractor, which reflects the *strongly damped property* of to some extent.

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Additional Information

**Meihua Yang**

Affiliation:
Department of Mathematics, Nanjing University, Nanjing, 210093, People’s Republic of China – and – Department of Mathematics, Huazhong University of Science and Technology, Wuhan, 430074, People’s Republic of China

Email:
yangmeih@gmail.com

**Chunyou Sun**

Affiliation:
Department of Mathematics, Lanzhou University, Lanzhou, 730000, People’s Republic of China – and – Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, 100080, People’s Republic of China

Email:
cysun@amss.ac.cn, sunchunyou@gmail.com

DOI:
http://dx.doi.org/10.1090/S0002-9947-08-04680-1

Keywords:
Strongly damped wave equation,
locally uniform spaces,
critical exponent,
asymptotic regularity,
attractors.

Received by editor(s):
May 18, 2007

Published electronically:
September 29, 2008

Additional Notes:
This work was supported by the NSFC Grants 10601021 and 10726024 and the China Postdoctoral Science Foundation.

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.