Asymptotics of linear initial boundary value problems with periodic boundary data on the half-line and finite intervals

Handle URI:
http://hdl.handle.net/10754/597627
Title:
Asymptotics of linear initial boundary value problems with periodic boundary data on the half-line and finite intervals
Authors:
Dujardin, G. M.
Abstract:
This paper deals with the asymptotic behaviour of the solutions of linear initial boundary value problems with constant coefficients on the half-line and on finite intervals. We assume that the boundary data are periodic in time and we investigate whether the solution becomes time-periodic after sufficiently long time. Using Fokas' transformation method, we show that, for the linear Schrödinger equation, the linear heat equation and the linearized KdV equation on the half-line, the solutions indeed become periodic for large time. However, for the same linear Schrödinger equation on a finite interval, we show that the solution, in general, is not asymptotically periodic; actually, the asymptotic behaviour of the solution depends on the commensurability of the time period T of the boundary data with the square of the length of the interval over. © 2009 The Royal Society.
Citation:
Dujardin GM (2009) Asymptotics of linear initial boundary value problems with periodic boundary data on the half-line and finite intervals. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465: 3341–3360. Available: http://dx.doi.org/10.1098/rspa.2009.0194.
Publisher:
The Royal Society
Journal:
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
KAUST Grant Number:
KUK-I1-007-43
Issue Date:
12-Aug-2009
DOI:
10.1098/rspa.2009.0194
Type:
Article
ISSN:
1364-5021; 1471-2946
Sponsors:
The author thanks A.S. Fokas and P.A. Markowich for their ideas and comments on this work. This publication is based on work supported by Award No. KUK-I1-007-43, made by the King Abdullah University of Science and Technology.
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Full metadata record

DC FieldValue Language
dc.contributor.authorDujardin, G. M.en
dc.date.accessioned2016-02-25T12:43:18Zen
dc.date.available2016-02-25T12:43:18Zen
dc.date.issued2009-08-12en
dc.identifier.citationDujardin GM (2009) Asymptotics of linear initial boundary value problems with periodic boundary data on the half-line and finite intervals. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465: 3341–3360. Available: http://dx.doi.org/10.1098/rspa.2009.0194.en
dc.identifier.issn1364-5021en
dc.identifier.issn1471-2946en
dc.identifier.doi10.1098/rspa.2009.0194en
dc.identifier.urihttp://hdl.handle.net/10754/597627en
dc.description.abstractThis paper deals with the asymptotic behaviour of the solutions of linear initial boundary value problems with constant coefficients on the half-line and on finite intervals. We assume that the boundary data are periodic in time and we investigate whether the solution becomes time-periodic after sufficiently long time. Using Fokas' transformation method, we show that, for the linear Schrödinger equation, the linear heat equation and the linearized KdV equation on the half-line, the solutions indeed become periodic for large time. However, for the same linear Schrödinger equation on a finite interval, we show that the solution, in general, is not asymptotically periodic; actually, the asymptotic behaviour of the solution depends on the commensurability of the time period T of the boundary data with the square of the length of the interval over. © 2009 The Royal Society.en
dc.description.sponsorshipThe author thanks A.S. Fokas and P.A. Markowich for their ideas and comments on this work. This publication is based on work supported by Award No. KUK-I1-007-43, made by the King Abdullah University of Science and Technology.en
dc.publisherThe Royal Societyen
dc.subjectApplied mathematicsen
dc.subjectDifferential equationsen
dc.subjectInitial boundary value problemsen
dc.subjectLong-time behaviouren
dc.subjectPeriodic dataen
dc.titleAsymptotics of linear initial boundary value problems with periodic boundary data on the half-line and finite intervalsen
dc.typeArticleen
dc.identifier.journalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciencesen
kaust.grant.numberKUK-I1-007-43en
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