Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Dimension of the global attractor for damped nonlinear wave equations
HTML articles powered by AMS MathViewer

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
  • Jack K. Hale, Asymptotic behavior of dissipative systems, Mathematical Surveys and Monographs, vol. 25, American Mathematical Society, Providence, RI, 1988. MR 941371, DOI 10.1090/surv/025
  • Roger Temam, Infinite-dimensional dynamical systems in mechanics and physics, Applied Mathematical Sciences, vol. 68, Springer-Verlag, New York, 1988. MR 953967, DOI 10.1007/978-1-4684-0313-8
  • G. Wang and S. Zhu, On dimension of the global attractor for damped sine-Gordon equation, Preprint, to appear in J. Math. Phys.
  • A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, vol. 44, Springer-Verlag, New York, 1983. MR 710486, DOI 10.1007/978-1-4612-5561-1
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 35B40, 35L70
  • Retrieve articles in all journals with MSC (1991): 35B40, 35L70
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