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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A damped hyperbolic equation on thin domains


Authors: Jack K. Hale and Geneviève Raugel
Journal: Trans. Amer. Math. Soc. 329 (1992), 185-219
MSC: Primary 58F12; Secondary 35K57, 35L70, 58D25
MathSciNet review: 1040261
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Abstract: For a damped hyperbolic equation in a thin domain in $ {{\mathbf{R}}^3}$ over a bounded smooth domain in $ {{\mathbf{R}}^2}$, it is proved that the global attractors are upper semicontinuous. It is shown also that a global attractor exists in the case of the critical Sobolev exponent.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1040261-1
PII: S 0002-9947(1992)1040261-1
Keywords: Hyperbolic equations, attractors thin domains
Article copyright: © Copyright 1992 American Mathematical Society