Fractal Dimension of a Random Invariant Set and Applications

We prove an abstract result on random invariant sets of finite fractal dimension. Then this result is applied to a stochastic semilinear degenerate parabolic equation and an upper bound is obtained for the random attractors of fractal dimension.

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Bibliographic Details
Published inJournal of Applied Mathematics Vol. 2013; no. 2013; pp. 113 - 117-310
Main Authors Wang, Gang, Tang, Yanbin
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Limiteds 01.01.2013
Hindawi Puplishing Corporation
Hindawi Publishing Corporation
John Wiley & Sons, Inc
Hindawi Limited
Subjects
Fractal analysis
Fractals
Invariants
Mathematical analysis
Mathematical research
Stochastic differential equations
Stochasticity
Upper bounds
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Summary:We prove an abstract result on random invariant sets of finite fractal dimension. Then this result is applied to a stochastic semilinear degenerate parabolic equation and an upper bound is obtained for the random attractors of fractal dimension.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:1110-757X
1687-0042
DOI:10.1155/2013/415764