HIGHER ORDER APPROXIMATIONS IN THE HEAT EQUATION AND THE TRUNCATED MOMENT PROBLEM

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dc.contributor.authorKim, Yong Jungko
dc.contributor.authorNi, Wei-Mingko
dc.date.accessioned2013-03-11T05:39:38Z-
dc.date.available2013-03-11T05:39:38Z-
dc.date.created2012-02-06-
dc.date.created2012-02-06-
dc.date.issued2009-02-
dc.identifier.citationSIAM JOURNAL ON MATHEMATICAL ANALYSIS, v.40, no.6, pp.2241 - 2261-
dc.identifier.issn0036-1410-
dc.identifier.urihttp://hdl.handle.net/10203/98405-
dc.description.abstractIn this paper, we employ linear combinations of n heat kernels to approximate solutions to the heat equation. We show that such approximations are of order O(t(1/2p - 2n+1/2)) in L(p)-norm, 1 <= p <= infinity, as t -> infinity. For positive solutions of the heat equation such approximations are achieved using the theory of truncated moment problems. For general sign-changing solutions these type of approximations are obtained by simply adding an auxiliary heat kernel. Furthermore, inspired by numerical computations, we conjecture that such approximations converge geometrically as n -> infinity for any fixed t > 0.-
dc.languageEnglish-
dc.publisherSIAM PUBLICATIONS-
dc.subjectSCALAR CONSERVATION-LAWS-
dc.subjectLARGE TIME BEHAVIOR-
dc.subjectASYMPTOTIC-BEHAVIOR-
dc.subjectDIFFUSION-EQUATIONS-
dc.subjectN-WAVES-
dc.subjectBURGERS-EQUATION-
dc.subjectCONVERGENCE-
dc.titleHIGHER ORDER APPROXIMATIONS IN THE HEAT EQUATION AND THE TRUNCATED MOMENT PROBLEM-
dc.typeArticle-
dc.identifier.wosid000265778800004-
dc.type.rimsART-
dc.citation.volume40-
dc.citation.issue6-
dc.citation.beginningpage2241-
dc.citation.endingpage2261-
dc.citation.publicationnameSIAM JOURNAL ON MATHEMATICAL ANALYSIS-
dc.identifier.doi10.1137/08071778X-
dc.contributor.localauthorKim, Yong Jung-
dc.contributor.nonIdAuthorNi, Wei-Ming-
dc.type.journalArticleArticle-
dc.subject.keywordAuthorheat equation-
dc.subject.keywordAuthormoments-
dc.subject.keywordAuthorasymptotics convergence rates-
dc.subject.keywordAuthorapproximation of an integral formula-
dc.subject.keywordAuthorheat kernel-
dc.subject.keywordPlusSCALAR CONSERVATION-LAWS-
dc.subject.keywordPlusLARGE TIME BEHAVIOR-
dc.subject.keywordPlusASYMPTOTIC-BEHAVIOR-
dc.subject.keywordPlusDIFFUSION-EQUATIONS-
dc.subject.keywordPlusN-WAVES-
dc.subject.keywordPlusBURGERS-EQUATION-
dc.subject.keywordPlusCONVERGENCE-
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