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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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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Abstract 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.
AbstractList 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.
Audience Academic
Author Tang, Yanbin
Wang, Gang
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crossref_primary_10_1155_2014_403528
crossref_primary_10_1155_2014_450289
crossref_primary_10_1155_2020_8864585
Cites_doi 10.1017/CBO9780511662201
10.1007/BF02219225
10.1016/S0021-7824(99)80001-4
10.1016/j.jde.2008.05.017
10.1023/A:1022605313961
10.1080/07362999708809490
10.1098/rspa.2006.1753
10.1016/j.nonrwa.2011.04.007
10.1016/j.matpur.2005.08.001
10.1007/BF01193705
10.3934/dcds.2000.6.875
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Copyright Copyright © 2013 Gang Wang and Yanbin Tang.
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Copyright 2013 Hindawi Publishing Corporation
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SubjectTerms Fractal analysis
Fractals
Invariants
Mathematical analysis
Mathematical research
Stochastic differential equations
Stochasticity
Upper bounds
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Title Fractal Dimension of a Random Invariant Set and Applications
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