DC Field | Value | Language |
---|---|---|
dc.contributor.author | Khoshnevisan, D | - |
dc.contributor.author | Kim, K | - |
dc.date.accessioned | 2017-07-19T13:00:08Z | - |
dc.date.available | 2017-07-19T13:00:08Z | - |
dc.date.created | 2017-01-01 | - |
dc.date.issued | 2015-09 | - |
dc.identifier.issn | 0002-9939 | - |
dc.identifier.uri | https://oasis.postech.ac.kr/handle/2014.oak/36753 | - |
dc.description.abstract | Consider the semilinear heat equation partial derivative(t)u = partial derivative(2)(x)u + lambda sigma(u)xi on the interval [0, L] with Dirichlet zero-boundary condition and a nice non-random initial function, where the forcing xi is space-time white noise and lambda > 0 denotes the level of the noise. We show that, when the solution is intermittent [that is, when inf(z) vertical bar sigma(z)/z vertical bar > 0], the expected L-2-energy of the solution grows at least as exp{c lambda(2)} and at most as exp{c lambda(4)} as lambda -> infinity. In the case that the Dirichlet boundary condition is replaced by a Neumann boundary condition, we prove that the L-2-energy of the solution is in fact of sharp exponential order exp{c lambda(4)}. We show also that, for a large family of one-dimensional randomly forced wave equations on R, the energy of the solution grows as exp{c lambda} as lambda -> infinity. Thus, we observe the surprising result that the stochastic wave equation is, quite typically, significantly less noise-excitable than its parabolic counterparts. | - |
dc.language | English | - |
dc.publisher | American Mathematical Society | - |
dc.relation.isPartOf | PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | - |
dc.title | NON-LINEAR NOISE EXCITATION AND INTERMITTENCY UNDER HIGH DISORDER | - |
dc.type | Article | - |
dc.identifier.doi | 10.1090/S0002-9939-2015-12517-8 | - |
dc.type.rims | ART | - |
dc.identifier.bibliographicCitation | PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, v.143, no.9, pp.4073 - 4083 | - |
dc.identifier.wosid | 000357042700034 | - |
dc.date.tcdate | 2019-02-01 | - |
dc.citation.endPage | 4083 | - |
dc.citation.number | 9 | - |
dc.citation.startPage | 4073 | - |
dc.citation.title | PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | - |
dc.citation.volume | 143 | - |
dc.contributor.affiliatedAuthor | Kim, K | - |
dc.identifier.scopusid | 2-s2.0-84932630702 | - |
dc.description.journalClass | 1 | - |
dc.description.journalClass | 1 | - |
dc.description.wostc | 7 | - |
dc.type.docType | Article | - |
dc.subject.keywordAuthor | Stochastic heat equation | - |
dc.subject.keywordAuthor | stochastic wave equation | - |
dc.subject.keywordAuthor | intermittency | - |
dc.subject.keywordAuthor | non-linear noise excitation | - |
dc.relation.journalWebOfScienceCategory | Mathematics, Applied | - |
dc.relation.journalWebOfScienceCategory | Mathematics | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Mathematics | - |
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