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dc.contributor.authorFokas, AS
dc.contributor.authorvan der Weele, MC
dc.date.accessioned2021-10-28T08:09:23Z
dc.date.available2021-10-28T08:09:23Z
dc.date.issued2021-11
dc.date.submitted2021-02-02
dc.identifier.issn0022-2526
dc.identifier.othersapm12452
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/329992
dc.descriptionFunder: Engineering and Physical Sciences Research Council; Id: http://dx.doi.org/10.13039/501100000266
dc.descriptionFunder: Foundation for Education and European Culture; Id: http://dx.doi.org/10.13039/501100005411
dc.descriptionFunder: Cambridge Trust; Id: http://dx.doi.org/10.13039/501100003343
dc.descriptionFunder: Christ's College, University of Cambridge; Id: http://dx.doi.org/10.13039/501100000590
dc.descriptionFunder: A.G. Leventis Foundation; Id: http://dx.doi.org/10.13039/501100004117
dc.description.abstractAbstract: This paper elaborates on a new approach for solving the generalized Dirichlet‐to‐Neumann map, in the large time limit, for linear evolution PDEs formulated on the half‐line with time‐periodic boundary conditions. First, by employing the unified transform (also known as the Fokas method) it can be shown that the solution becomes time‐periodic for large t . Second, it is shown that the coefficients of the Fourier series of the unknown boundary values can be determined explicitly in terms of the coefficients of the Fourier series of the given boundary data in a very simple, algebraic way. This approach is illustrated for second‐order linear evolution equations and also for linear evolution equations containing spatial derivatives of arbitrary order. The simple and explicit determination of the unknown boundary values is based on the “ Q ‐equation”, which for the linearized nonlinear Schrödinger equation is the linear limit of the quadratic Q ‐equation introduced by Lenells and Fokas [Proc. R. Soc. A, 471, 2015]. Regarding the latter equation, it is also shown here that it provides a very simple, algebraic way for rederiving the remarkable results of Boutet de Monvel, Kotlyarov, and Shepelsky [Int. Math. Res. Not. issue 3, 2009] for the particular boundary condition of a single exponential.
dc.languageen
dc.publisherWiley
dc.subjectSPECIAL ISSUE
dc.subjectDirichlet‐to‐Neumann map
dc.subjectpartial differential equations
dc.subjectunified transform
dc.titleThe unified transform for evolution equations on the half‐line with time‐periodic boundary conditions*
dc.typeArticle
dc.date.updated2021-10-28T08:09:22Z
prism.publicationNameStudies in Applied Mathematics
dc.identifier.doi10.17863/CAM.77436
rioxxterms.versionofrecord10.1111/sapm.12452
rioxxterms.versionAO
rioxxterms.versionVoR
rioxxterms.licenseref.urihttp://creativecommons.org/licenses/by/4.0/
dc.contributor.orcidFokas, AS [0000-0002-5881-802X]
dc.contributor.orcidvan der Weele, MC [0000-0002-5792-2650]
dc.identifier.eissn1467-9590
pubs.funder-project-idAlexander S. Onassis Public Benefit Foundation (F ZQ 004‐1/2020‐2021)
cam.issuedOnline2021-10-27


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