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.
Saved in:
Published in | Journal of Applied Mathematics Vol. 2013; no. 2013; pp. 113 - 117-310 |
---|---|
Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Cairo, Egypt
Hindawi Limiteds
01.01.2013
Hindawi Puplishing Corporation Hindawi Publishing Corporation John Wiley & Sons, Inc Hindawi Limited |
Subjects | |
Online Access | Get full text |
Cover
Loading…
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 |
Author_xml | – sequence: 1 fullname: Wang, Gang – sequence: 2 fullname: Tang, Yanbin |
BookMark | eNqFkc-L1DAUx4us4O7qybPQoyjdfS8_mgQ8OIyuDgy4qAvewps0XTO0zZh2FP97M9thxJPJ4SXf98k3Id-L4myIgy-K5whXiFJeM0B-LVCqWjwqzrHWqgIQ7CyvEaFSUn17UlyM4xaAgTR4Xry5SeQm6sp3offDGOJQxrak8jMNTezL1fCTUqBhKr_4qcxaudjtuuBoyuT4tHjcUjf6Z8d6WdzdvP-6_FitP31YLRfriqSRU0Vca1B6Y4xTYuM3NbXao0fpG71xjRJatrVi2mnTCmBknOC81kY0aDgwzS-L1ezbRNraXQo9pd82UrAPQkz3ltIUXOctl-Q2DAW41ok8tBLEpVJGIJA2Pnu9nb12KW69m_zedaH5x3R5tz6qx7Kl3iI3QoNGg9ni5cnix96Pk-3D6HzX0eDjfrQoGRhec3lAr2b0nvLjwtDGKf93no3vg8vhtSHrC65qLTlnhwOv5wMuxXFMvj29DMEeMraHjO2ccaZfzfT3MDT0K_wHfjHDPiO-pRMsFHANuX879ymkMAW7jfs05FjtbXapwYAGwAdHZHaWkMFR-7vBfCOishyB_wGH5cOZ |
CitedBy_id | crossref_primary_10_1063_1_5085894 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 |
ContentType | Journal Article |
Contributor | Tang, Yanbin |
Contributor_xml | – sequence: 1 fullname: Tang, Yanbin |
Copyright | Copyright © 2013 Gang Wang and Yanbin Tang. COPYRIGHT 2013 John Wiley & Sons, Inc. Copyright 2013 Hindawi Publishing Corporation |
Copyright_xml | – notice: Copyright © 2013 Gang Wang and Yanbin Tang. – notice: COPYRIGHT 2013 John Wiley & Sons, Inc. – notice: Copyright 2013 Hindawi Publishing Corporation |
DBID | 188 ADJCN RHU RHW RHX AAYXX CITATION 7TB 8FD FR3 KR7 DOA |
DOI | 10.1155/2013/415764 |
DatabaseName | Chinese Electronic Periodical Services (CEPS) الدوريات العلمية والإحصائية - e-Marefa Academic and Statistical Periodicals Hindawi Publishing Complete Hindawi Publishing Subscription Journals Open Access: Hindawi Publishing CrossRef Mechanical & Transportation Engineering Abstracts Technology Research Database Engineering Research Database Civil Engineering Abstracts DOAJ Directory of Open Access Journals |
DatabaseTitle | CrossRef Civil Engineering Abstracts Engineering Research Database Technology Research Database Mechanical & Transportation Engineering Abstracts |
DatabaseTitleList | Civil Engineering Abstracts CrossRef |
Database_xml | – sequence: 1 dbid: RHX name: Open Access: Hindawi Publishing url: http://www.hindawi.com/journals/ sourceTypes: Publisher – sequence: 2 dbid: DOA name: DOAJ Directory of Open Access Journals url: https://www.doaj.org/ sourceTypes: Open Website |
DeliveryMethod | fulltext_linktorsrc |
Discipline | Applied Sciences |
EISSN | 1687-0042 |
Editor | Van Vleck, Erik |
Editor_xml | – sequence: 1 givenname: Erik surname: Van Vleck fullname: Van Vleck, Erik |
EndPage | 117-310 |
ExternalDocumentID | oai_doaj_org_article_35acb2140cfc4444874a35779410a89e oai_CULeuclid_euclid_jam_1394808191 A376853321 10_1155_2013_415764 470380 P20160908001_201312_201609120001_201609120001_113_117_310 |
GroupedDBID | -~9 188 24P 29J 2UF 2WC 3V. 4.4 5GY 5VS 70C 8FE 8FG 8R4 8R5 AAFWJ AAJEY AAOJF ABCQX ABDBF ABJCF ABUWG ACIPV ACIWK ADBBV AESBA AFFOW AFKRA AFPKN AHIZY AINHJ ALMA_UNASSIGNED_HOLDINGS ARAPS BCNDV BENPR BGLVJ BPHCQ CCPQU CNMHZ CS3 CVCKV CWDGH E3Z EBS EJD ESX GROUPED_DOAJ H13 HCIFZ HDK I-F IAO IL9 IPNFZ ITC J9A K6V K7- KQ8 L6V L7B M7S M~E OK1 P2P P62 PIMPY PQQKQ PROAC PTHSS PUASD Q2X RBF REI REM RHU RHX RIG RNS RPE TR2 TUS UPT UZ4 WS9 YQT ~8M ADJCN C1A RHW AAYXX CITATION 7TB 8FD FR3 KR7 9 AALRV AARKR ABPTK ACJDT ADACO AGFPJ PQEST PQUKI PRINS |
ID | FETCH-LOGICAL-a595t-a388078b99c74beb6af8e1e15ed8bcd7485f6728c89f402a9c4336894d1930283 |
IEDL.DBID | DOA |
ISSN | 1110-757X |
IngestDate | Mon Oct 07 19:36:01 EDT 2024 Tue Jan 05 18:13:24 EST 2021 Fri Aug 16 01:50:56 EDT 2024 Tue Oct 15 04:50:19 EDT 2024 Fri Aug 23 03:14:50 EDT 2024 Sun Jun 02 18:48:55 EDT 2024 Thu Sep 12 21:34:53 EDT 2024 Tue Oct 01 22:52:04 EDT 2024 |
IsDoiOpenAccess | true |
IsOpenAccess | true |
IsPeerReviewed | true |
IsScholarly | true |
Issue | 2013 |
Language | English |
License | This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
LinkModel | DirectLink |
MergedId | FETCHMERGED-LOGICAL-a595t-a388078b99c74beb6af8e1e15ed8bcd7485f6728c89f402a9c4336894d1930283 |
Notes | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
ORCID | 0000-0001-6287-5273 |
OpenAccessLink | https://doaj.org/article/35acb2140cfc4444874a35779410a89e |
PQID | 1520936351 |
PQPubID | 23500 |
ParticipantIDs | doaj_primary_oai_doaj_org_article_35acb2140cfc4444874a35779410a89e projecteuclid_primary_oai_CULeuclid_euclid_jam_1394808191 proquest_miscellaneous_1520936351 gale_infotracacademiconefile_A376853321 crossref_primary_10_1155_2013_415764 hindawi_primary_10_1155_2013_415764 emarefa_primary_470380 airiti_journals_P20160908001_201312_201609120001_201609120001_113_117_310 |
PublicationCentury | 2000 |
PublicationDate | 2013-01-01 |
PublicationDateYYYYMMDD | 2013-01-01 |
PublicationDate_xml | – month: 01 year: 2013 text: 2013-01-01 day: 01 |
PublicationDecade | 2010 |
PublicationPlace | Cairo, Egypt |
PublicationPlace_xml | – name: Cairo, Egypt |
PublicationTitle | Journal of Applied Mathematics |
PublicationYear | 2013 |
Publisher | Hindawi Limiteds Hindawi Puplishing Corporation Hindawi Publishing Corporation John Wiley & Sons, Inc Hindawi Limited |
Publisher_xml | – name: Hindawi Limiteds – name: Hindawi Puplishing Corporation – name: Hindawi Publishing Corporation – name: John Wiley & Sons, Inc – name: Hindawi Limited |
References | (4) 1994; 100 Babin A. V. Vishik M. I. Attractors of Evolution Equations 1992 25 Amsterdam, The Netherlands North-Holland MR1156492 Temam R. Infinite-Dimensional Dynamical Systems in Mechanics and Physics 1997 68 2nd New York, NY, USA Springer MR1441312 (9) 2011; 12 Arnold L. Random Dynamical Systems 1998 Berlin, Germany Springer MR1723992 (5) 2009; 246 (12) 1998; 77 (6) 1997; 9 (8) 2007; 463 Chueshov I. Lasiecka I. Long-time behavior of second order evolution equations with nonlinear damping Memoirs of the American Mathematical Society 2008 195 Providence, RI, USA American Mathematical Society Hale J. K. Asymptotic Behavior of Dissipative Systems 1988 25 Providence, RI, USA American Mathematical Society MR941371 (7) 2000; 6 (10) 1998; 10 Falconer K. Fractal Geometry 1990 Chichester, UK John Wiley & Sons MR1102677 (11) 1997; 15 (13) 2006; 85 Edmunds D. E. Triebel H. Function Spaces, Entropy Numbers, Differential Operators 1996 120 New York, NY, USA Cambridge University Press Cambridge Tracts in Mathematics 10.1017/CBO9780511662201 MR1410258 11 12 (17) 1997; 68 15 16 18 (4) 1992; 25 (14) 1988; 25 3 5 6 7 (8) 2008; 195 9 (13) 1990 10 (2) 1998 |
References_xml | – volume: 100 start-page: 365 issue: 3 year: 1994 end-page: 393 ident: 4 article-title: Attractors for random dynamical systems publication-title: – volume: 6 start-page: 875 issue: 4 year: 2000 end-page: 892 ident: 7 article-title: Stability and random attractors for a reaction-diffusion equation with multiplicative noise publication-title: – volume: 246 start-page: 845 issue: 2 year: 2009 end-page: 869 ident: 5 article-title: Random attractors for stochastic reaction-diffusion equations on unbounded domains publication-title: – volume: 12 start-page: 2811 issue: 5 year: 2011 end-page: 2821 ident: 9 article-title: Random attractors for stochastic semi-linear degenerate parabolic equations publication-title: – volume: 10 start-page: 449 issue: 3 year: 1998 end-page: 474 ident: 10 article-title: Hausdorff dimension of invariant sets for random dynamical systems publication-title: – volume: 9 start-page: 307 issue: 2 year: 1997 end-page: 341 ident: 6 article-title: Random attractors publication-title: – volume: 77 start-page: 967 issue: 10 year: 1998 end-page: 988 ident: 12 article-title: Hausdorff dimension of a random invariant set publication-title: – volume: 463 start-page: 163 issue: 2077 year: 2007 end-page: 181 ident: 8 article-title: Flattening, squeezing and the existence of random attractors publication-title: – volume: 15 start-page: 473 issue: 4 year: 1997 end-page: 491 ident: 11 article-title: On the finite dimensionality of random attractors publication-title: – volume: 85 start-page: 269 issue: 2 year: 2006 end-page: 294 ident: 13 article-title: Fractal dimension of a random invariant set publication-title: – volume: 195 volume-title: Long-time behavior of second order evolution equations with nonlinear damping year: 2008 ident: 8 – ident: 12 doi: 10.1017/CBO9780511662201 – ident: 5 doi: 10.1007/BF02219225 – ident: 11 doi: 10.1016/S0021-7824(99)80001-4 – ident: 3 doi: 10.1016/j.jde.2008.05.017 – ident: 7 doi: 10.1023/A:1022605313961 – year: 1998 ident: 2 – ident: 10 doi: 10.1080/07362999708809490 – ident: 16 doi: 10.1098/rspa.2006.1753 – volume: 25 year: 1988 ident: 14 – ident: 18 doi: 10.1016/j.nonrwa.2011.04.007 – volume: 25 year: 1992 ident: 4 – ident: 15 doi: 10.1016/j.matpur.2005.08.001 – year: 1990 ident: 13 – volume: 68 year: 1997 ident: 17 – ident: 6 doi: 10.1007/BF01193705 – ident: 9 doi: 10.3934/dcds.2000.6.875 |
SSID | ssj0020591 |
Score | 2.1473117 |
Snippet | We prove an abstract result on random invariant sets of finite fractal dimension. Then this result is applied to a stochastic semilinear degenerate parabolic... |
SourceID | doaj projecteuclid proquest gale crossref hindawi emarefa airiti |
SourceType | Open Website Open Access Repository Aggregation Database Publisher |
StartPage | 113 |
SubjectTerms | Fractal analysis Fractals Invariants Mathematical analysis Mathematical research Stochastic differential equations Stochasticity Upper bounds |
SummonAdditionalLinks | – databaseName: Open Access: Hindawi Publishing dbid: RHX link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV1bixMxFA7uguCL98XxRsQFnwabmWSSgC91tXRFRVYLfQtncmEr7lTsVP--58xki3VB7EuZMJdwLjnnS3K-MHYsg6hCAF9O2oAAJRlR2uhjCcK3aRJl6wOt6H742MwX8t1SLfMG2c3VJXyMdgjPRf0S44xu5AE7MIYY8s_myx2swgRhgFUYyEqt9DJX4f31KEYYWBFP0F4AGnj6h2JcwGvYjcvXzwkR_1rRVslxRiRu_bdVuDJiD2FodpvdzPkjn44Kv8Ouxe4uu5VzSZ49dXOPvZpR-RPe-Ybo-2lKjK8TB34GXVhf8NPuJ4JklCr_HHuObXz6x0r2fbaYvf1yMi_zSQklKKv6EojSRZvWWq9lG9sGkokiChWDQWlraVRqdGW8sQkBI1gv67oxFjVla8owjthht-7iA8aF8NZIiLERIAM-H33SgLBChJBSMynY6ShHl4194z5VRFNnKfcUjkQuKjc2CSoEEvsXQtTEMO4wryzY8aUq3PeRXMMNoESp4T1uVF3BXpOadrcQI_bQgFbisoO5WoFvK4SLPnmJP6Ml1ErjcCMmYGws2FFW8u49Ekc7g514QTp35NA9qgZyXQKKg6ix3BSHYMxp6koU7Hk2i3_31u6ZzF63Txbvc2v--woXDpNwSQegWPzCs0vzcujmtHYDXVxvN07QdqUas0Px8L968YjdqIaDO2iy6DE77H9s4xNMn_r26eA9vwF-ewsK priority: 102 providerName: Hindawi Publishing |
Title | Fractal Dimension of a Random Invariant Set and Applications |
URI | https://www.airitilibrary.com/Article/Detail/P20160908001-201312-201609120001-201609120001-113-117-310 https://search.emarefa.net/detail/BIM-470380 https://dx.doi.org/10.1155/2013/415764 https://search.proquest.com/docview/1520936351 http://projecteuclid.org/euclid.jam/1394808191 https://doaj.org/article/35acb2140cfc4444874a35779410a89e |
Volume | 2013 |
hasFullText | 1 |
inHoldings | 1 |
isFullTextHit | |
isPrint | |
link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1bb9MwFLZggLQX7hPhUgUxiadoPYmd2BIv2WjpJpimQqXyZDm2oxVtKaIp_H3OSdxqFRK80IdEsdLEORf7fLbPZ8YOuYPUOWOTYeUQoNQSEuWtTwzYqh56XllHM7qfzvPJjJ_NxfzGVl-0JqynB-4Fd5QJY6sUYYCtLcefLLjJRIFmBEMjle9aXxAbMBWgFgYNHdTCzi0pRDEPmXnYeSLah-wIu62CSAbumgVxB-10Sh13f5ega_DabNvqe5eEkn8taPlkP0ri1_Zq4f5oxbuuafyQ3Q8xZVz23_KI3fLNY_YgxJdx8N7VE_ZuTClReOd7ovSnYbJ4WccmnprGLa_j0-YnAmeUdPzZtzGWxeWN2e2nbDYefTmZJGH3hMQIJdrEEM1LISulbMErX-Wmlh48CO8kaqDgUtR5kUorVY0g0ijLsyyXCrWnMoo6Dthes2z8MxYDWCW58T4Hwx3-39u6MAg1wLm6zocRO-3lqIMDrPRFStR1iuJR0CRySHVfBJQcBLsXABmxjmuMNSN2uFGF_t4TbugOqAjRPUf3qovYMalpewuxZHcFaDs62I7-l-1E7CAoefscji2gxEq8JZ1rcvIWVWNCrgKKg-iydInNMsY5WQoRexPM4u-1VTsms1Ptk9nHUBpO38y1xsCc06YoCt_wemNeGl2f5nNM45frlQZawpRhxAjP_4c0XrD9tNvrg8aXXrK99sfav8KIq60G7LYcfxiwO2V5NvqK5-PR-cV00LkcHqeT-W8z3CJF |
link.rule.ids | 230,315,786,790,869,870,883,884,889,891,2115,27955,27956,33407,33778 |
linkProvider | Directory of Open Access Journals |
openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Fractal+Dimension+of+a+Random+Invariant+Set+and+Applications&rft.jtitle=Journal+of+applied+mathematics&rft.au=Wang%2C+Gang&rft.au=Tang%2C+Yanbin&rft.date=2013-01-01&rft.pub=Hindawi+Publishing+Corporation&rft.eissn=1687-0042&rft_id=info:doi/10.1155%2F2013%2F415764&rft.externalDBID=jam&rft.externalDocID=oai_CULeuclid_euclid_jam_1394808191 |
thumbnail_m | http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=https%3A%2F%2Fwww.airitilibrary.com%2Fjnltitledo%2FP20160908001-c.jpg |