DC Field | Value | Language |
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dc.contributor.author | Khoshnevisan, Davar | - |
dc.contributor.author | Kim, Kunwoo | - |
dc.contributor.author | Xiao, Yimin | - |
dc.date.accessioned | 2019-02-25T04:12:52Z | - |
dc.date.available | 2019-02-25T04:12:52Z | - |
dc.date.created | 2018-06-12 | - |
dc.date.issued | 2018-05 | - |
dc.identifier.issn | 0010-3616 | - |
dc.identifier.uri | https://oasis.postech.ac.kr/handle/2014.oak/94688 | - |
dc.description.abstract | It is generally argued that the solution to a stochastic PDE with multiplicative noise-such as , where denotes space-time white noise-routinely produces exceptionally-large peaks that are "macroscopically multifractal." See, for example, Gibbon and Doering (Arch Ration Mech Anal 177:115-150, 2005), Gibbon and Titi (Proc R Soc A 461:3089-3097, 2005), and Zimmermann et al. (Phys Rev Lett 85(17):3612-3615, 2000). A few years ago, we proved that the spatial peaks of the solution to the mentioned stochastic PDE indeed form a random multifractal in the macroscopic sense of Barlow and Taylor (J Phys A 22(13):2621-2626, 1989; Proc Lond Math Soc (3) 64:125-152, 1992). The main result of the present paper is a proof of a rigorous formulation of the assertion that the spatio-temporal peaks of the solution form infinitely-many different multifractals on infinitely-many different scales, which we sometimes refer to as "stretch factors." A simpler, though still complex, such structure is shown to also exist for the constant-coefficient version of the said stochastic PDE. | - |
dc.language | English | - |
dc.publisher | SPRINGER | - |
dc.relation.isPartOf | COMMUNICATIONS IN MATHEMATICAL PHYSICS | - |
dc.title | A Macroscopic Multifractal Analysis of Parabolic Stochastic PDEs | - |
dc.type | Article | - |
dc.identifier.doi | 10.1007/s00220-018-3136-6 | - |
dc.type.rims | ART | - |
dc.identifier.bibliographicCitation | COMMUNICATIONS IN MATHEMATICAL PHYSICS, v.360, no.1, pp.307 - 346 | - |
dc.identifier.wosid | 000431030400007 | - |
dc.citation.endPage | 346 | - |
dc.citation.number | 1 | - |
dc.citation.startPage | 307 | - |
dc.citation.title | COMMUNICATIONS IN MATHEMATICAL PHYSICS | - |
dc.citation.volume | 360 | - |
dc.contributor.affiliatedAuthor | Kim, Kunwoo | - |
dc.identifier.scopusid | 2-s2.0-85045238351 | - |
dc.description.journalClass | 1 | - |
dc.description.journalClass | 1 | - |
dc.type.docType | Article | - |
dc.subject.keywordPlus | PARTIAL-DIFFERENTIAL-EQUATIONS | - |
dc.subject.keywordPlus | HEAT-EQUATION | - |
dc.subject.keywordPlus | INTERMITTENCY | - |
dc.subject.keywordPlus | NOISE | - |
dc.subject.keywordPlus | INTERFACES | - |
dc.relation.journalWebOfScienceCategory | Physics, Mathematical | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Physics | - |
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