DC Field | Value | Language |
---|---|---|
dc.contributor.author | Khoshnevisan, Davar | - |
dc.contributor.author | Kim, Kunwoo | - |
dc.contributor.author | Mueller, Carl | - |
dc.contributor.author | Shiu, Shang-Yuan | - |
dc.date.accessioned | 2024-06-20T07:00:59Z | - |
dc.date.available | 2024-06-20T07:00:59Z | - |
dc.date.created | 2023-12-11 | - |
dc.date.issued | 2023-07 | - |
dc.identifier.issn | 1083-6489 | - |
dc.identifier.uri | https://oasis.postech.ac.kr/handle/2014.oak/123673 | - |
dc.description.abstract | We consider a reaction-diffusion equation of the type partial differential t0 = partial differential x20 + V (0) + & lambda;& sigma; (0)W on (0, & INFIN;) x T, subject to a "nice" initial value and periodic boundary, where T = [-1 , 1] and denotes space-time white noise. The reaction term V : l & RARR; l belongs to a large family of functions that includes Fisher-KPP nonlinearities [V (x) = x(1 - x)] as well as Allen-Cahn potentials [V (x) = x(1 - x)(1 + x)], the multiplicative nonlinearity & sigma; : l & RARR; l is non random and Lipschitz continuous, and & lambda; > 0 is a non-random number that measures the strength of the effect of the noise W. The principal finding of this paper is that: (i) When & lambda; is sufficiently large, the above equation has a unique invariant measure; and (ii) When & lambda; is sufficiently small, the collection of all invariant measures is a non-trivial line segment, in particular infinite. This proves an earlier prediction of Zimmerman et al. (2000). Our methods also say a great deal about the structure of these invariant measures. W | - |
dc.language | English | - |
dc.publisher | Institute of Mathematical Statistics | - |
dc.relation.isPartOf | Electronic Journal of Probability | - |
dc.title | Phase analysis for a family of stochastic reaction-diffusion equations | - |
dc.type | Article | - |
dc.identifier.doi | 10.1214/23-EJP983 | - |
dc.type.rims | ART | - |
dc.identifier.bibliographicCitation | Electronic Journal of Probability, v.28 | - |
dc.identifier.wosid | 001049620500001 | - |
dc.citation.title | Electronic Journal of Probability | - |
dc.citation.volume | 28 | - |
dc.contributor.affiliatedAuthor | Kim, Kunwoo | - |
dc.identifier.scopusid | 2-s2.0-85169708062 | - |
dc.description.journalClass | 1 | - |
dc.description.journalClass | 1 | - |
dc.description.isOpenAccess | Y | - |
dc.type.docType | Article | - |
dc.subject.keywordPlus | HEAT-EQUATION | - |
dc.subject.keywordPlus | NOISE | - |
dc.subject.keywordAuthor | stochastic partial differential equations | - |
dc.subject.keywordAuthor | invariant measures | - |
dc.subject.keywordAuthor | phase transition | - |
dc.relation.journalWebOfScienceCategory | Statistics & Probability | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
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