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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Dimension of the global attractor for damped nonlinear wave equations
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by Zhou Shengfan PDF
Proc. Amer. Math. Soc. 127 (1999), 3623-3631 Request permission

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
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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
  • 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
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 3623-3631
  • MSC (1991): Primary 35B40, 35L70
  • DOI: https://doi.org/10.1090/S0002-9939-99-05121-7
  • MathSciNet review: 1637385