Mathematical Methods in the Applied Sciences

Volume 38, Issue 8 pp. 1557-1567

Research Article

Asymptotic behavior for the singularly perturbed damped Boussinesq equation

Ke Li,

Corresponding Author

Ke Li

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

Correspondence to: Ke Li, School of Mathematics and Statistics, Zhengzhou University, China.

E-mail: [email protected]

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Zhijian Yang,

Zhijian Yang

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

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Ke Li,

Corresponding Author

Ke Li

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

Correspondence to: Ke Li, School of Mathematics and Statistics, Zhengzhou University, China.

E-mail: [email protected]

Search for more papers by this author

Zhijian Yang,

Zhijian Yang

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

Search for more papers by this author

First published: 13 May 2014

https://doi.org/10.1002/mma.3167

Citations: 3

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Abstract

This work is focused on the long-time behavior of solutions to the singularly perturbed damped Boussinesq equation in a 3D case

$urn:x-wiley:1704214:media:mma3167:mma3167-math-0001$

where ε > 0 is small enough. Without any growth restrictions on the nonlinearity f(u), we establish in an appropriate bounded phase space a finite dimensional global attractor as well as an exponential attractor of optimal regularity. The key step is the estimate of the difference between the solutions of the damped Boussinesq equation and the corresponding pseudo-parabolic equation.Copyright © 2014 John Wiley & Sons, Ltd.

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Volume38, Issue8

30 May 2015

Pages 1557-1567

Asymptotic behavior for the singularly perturbed damped Boussinesq equation

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Asymptotic behavior for the singularly perturbed damped Boussinesq equation

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