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

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- by Meihua Yang and Chunyou Sun PDF
- Trans. Amer. Math. Soc.
**361**(2009), 1069-1101 Request permission

## 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 op- timal and the existence of a bounded (in $H^2_{lu}(\mathbb {R}^N)\times H^1_{lu}(\mathbb {R}^N)$) subset which attracts exponentially every initial $H^1_{lu}(\mathbb {R}^N)\times L^2_{lu}(\mathbb {R}^N)$-bounded set with respect to the $H^1_{lu}(\mathbb {R}^N)\times L^2_{lu}(\mathbb {R}^N)$-norm. Then, we show there is a $(H ^1_{lu}(\mathbb {R}^N)\times L^2_{lu}(\mathbb {R}^N), H^1_\rho (\mathbb {R}^N)\times H^1_\rho (\mathbb {R}^N))$-global attractor, which reflects the*strongly damped property*of $\Delta u_t$ 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
- ORCID: 0000-0003-3770-7651
- Email: cysun@amss.ac.cn, sunchunyou@gmail.com
- 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.
- © Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc.
**361**(2009), 1069-1101 - MSC (2000): Primary 37L05, 35B40, 35B41
- DOI: https://doi.org/10.1090/S0002-9947-08-04680-1
- MathSciNet review: 2452835