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A note on the dimension of the global attractor for an abstract semilinear hyperbolic problem
Type of publication: Article
Citation: 2007-34
Publication status: Published
Journal: Applied Mathematics Letters
Volume: 22
Number: 7
Year: 2009
Pages: 1025--1028
Note: Preprint no. 2007-34
ISSN: 0893-9659
URL: http://www.karlin.mff.cuni.cz/...
DOI: 10.1016/j.aml.2009.01.027
Abstract: We study a semilinear hyperbolic problem, written as a second-order evolution equation in an infinite-dimensional Hilbert space. Assuming existence of the global attractor, we estimate its fractal dimension explicitly in terms of the data. Despite its elementary character, our technique gives reasonable results. Notably, we require no additional regularity, although nonlinear damping is allowed.
Userfields: fjournal={Applied Mathematics Letters. An International Journal of Rapid Publication}, coden={AMLEEL}, mrclass={35B41 (34D45 34G20 35L70 37L30)}, mrnumber={MR2522993},
Keywords: Dimension of attractor, fractal dimension, Method of ℓ-trajectories, Nonlinear hyperbolic problem, Squeezing property
Authors Bulíček, Miroslav
Pražák, Dalibor
Added by: [ADM]
Total mark: 0
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