There are no files associated with this item.
Full metadata record
DC Field | Value | Language |
---|---|---|
dc.citation.endPage | 2139 | - |
dc.citation.number | 4 | - |
dc.citation.startPage | 2087 | - |
dc.citation.title | ANNALS OF PROBABILITY | - |
dc.citation.volume | 47 | - |
dc.contributor.author | Kim, Ildoo | - |
dc.contributor.author | Kim, Kyeong-Hun | - |
dc.contributor.author | Lim, Sungbin | - |
dc.date.accessioned | 2023-12-21T18:56:13Z | - |
dc.date.available | 2023-12-21T18:56:13Z | - |
dc.date.created | 2020-01-20 | - |
dc.date.issued | 2019-07 | - |
dc.description.abstract | In this article, we present an L-p-theory (p >= 2) for the semi-linear stochastic partial differential equations (SPDEs) of type partial derivative(alpha)(t)u = L(omega,t,x)u + f(u) + partial derivative(beta)(t) Sigma(infinity)(k=1)integral(t)(0)(Lambda(k)(omega,t,x)u + g(k)(u)) dw(t)(k), where alpha is an element of (0,2), beta < alpha + 1/2 and partial derivative(alpha)(t) and partial derivative(beta)(t) denote the Caputo derivatives of order alpha and beta, respectively. The processes omega(k)(t), k is an element of N={1,2, . . . }, are independent one-dimensional Wiener processes, L is either divergence or nondivergence-type second-order operator, and Lambda(k) are linear operators of order up to two. This class of SPDEs can be used to describe random effects on transport of particles in medium with thermal memory or particles subject to sticking and trapping. We prove uniqueness and existence results of strong solutions in appropriate Sobolev spaces, and obtain maximal L-p-regularity of the solutions. By converting SPDEs driven by d-dimensional space-time white noise into the equations of above type, we also obtain an L-p-theory for SPDEs driven by space-time white noise if the space dimension d < 4 - 2(2 beta -1)alpha(-1). In particular, if beta < 1/2 + alpha/4 then we can handle space-time white noise driven SPDEs with space dimension d = 1, 2, 3. | - |
dc.identifier.bibliographicCitation | ANNALS OF PROBABILITY, v.47, no.4, pp.2087 - 2139 | - |
dc.identifier.doi | 10.1214/18-AOP1303 | - |
dc.identifier.issn | 0091-1798 | - |
dc.identifier.scopusid | 2-s2.0-85075854930 | - |
dc.identifier.uri | https://scholarworks.unist.ac.kr/handle/201301/30829 | - |
dc.identifier.url | https://projecteuclid.org/euclid.aop/1562205704 | - |
dc.identifier.wosid | 000474204900007 | - |
dc.language | 영어 | - |
dc.publisher | INST MATHEMATICAL STATISTICS | - |
dc.title | A SOBOLEV SPACE THEORY FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH TIME-FRACTIONAL DERIVATIVES | - |
dc.type | Article | - |
dc.description.isOpenAccess | FALSE | - |
dc.relation.journalWebOfScienceCategory | Statistics & Probability | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.type.docType | Article | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.subject.keywordAuthor | Stochastic partial differential equations | - |
dc.subject.keywordAuthor | time fractional derivatives | - |
dc.subject.keywordAuthor | maximal L-p-regularity | - |
dc.subject.keywordAuthor | multidimensional space-time white noise | - |
dc.subject.keywordPlus | EVOLUTION-EQUATIONS | - |
dc.subject.keywordPlus | MAXIMAL REGULARITY | - |
dc.subject.keywordPlus | DIFFUSION | - |
dc.subject.keywordPlus | INEQUALITY | - |
Items in Repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Tel : 052-217-1404 / Email : scholarworks@unist.ac.kr
Copyright (c) 2023 by UNIST LIBRARY. All rights reserved.
ScholarWorks@UNIST was established as an OAK Project for the National Library of Korea.