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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Dimension of the global attractor
for damped nonlinear wave equations


Author: Zhou Shengfan
Journal: Proc. Amer. Math. Soc. 127 (1999), 3623-3631
MSC (1991): Primary 35B40, 35L70
Published electronically: May 17, 1999
MathSciNet review: 1637385
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Abstract | References | Similar Articles | Additional Information

Abstract: An estimate on the Hausdorff dimension of the global attractor for damped nonlinear wave equations, in two cases of nonlinear damping and linear damping, with Dirichlet boundary condition is obtained. The gained Hausdorff dimension is bounded and is independent of the concrete form of nonlinear damping term. In the case of linear damping, the gained Hausdorff dimension remains small for large damping, which conforms to the physical intuition.


References [Enhancements On Off] (What's this?)

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Additional Information

Zhou Shengfan
Affiliation: Department of Mathematics, Sichuan Union University, Chengdu, 610064, People’s Republic of China
Email: nic2601@scuu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05121-7
PII: S 0002-9939(99)05121-7
Keywords: Wave equation, global attractor, Hausdorff dimension
Received by editor(s): February 19, 1998
Published electronically: May 17, 1999
Additional Notes: This research was supported by the National Natural Science Foundation of China
Communicated by: Michael Handel
Article copyright: © Copyright 1999 American Mathematical Society