The Fundamental k-Form and Global Relations

dc.contributor.authorAnthony C.L. Ashton
dc.date.accessioned2019-02-19T12:24:52Z
dc.date.available2019-02-19T12:24:52Z
dc.date.issued2008
dc.description.abstractIn [Proc. Roy. Soc. London Ser. A 453 (1997), no. 1962, 1411-1443] A.S. Fokas introduced a novel method for solving a large class of boundary value problems associated with evolution equations. This approach relies on the construction of a so-called global relation: an integral expression that couples initial and boundary data. The global relation can be found by constructing a differential form dependent on some spectral parameter, that is closed on the condition that a given partial differential equation is satisfied. Such a differential form is said to be fundamental [Quart. J. Mech. Appl. Math. 55 (2002), 457-479]. We give an algorithmic approach in constructing a fundamental k-form associated with a given boundary value problem, and address issues of uniqueness. Also, we extend a result of Fokas and Zyskin to give an integral representation to the solution of a class of boundary value problems, in an arbitrary number of dimensions. We present an extended example using these results in which we construct a global relation for the linearised Navier-Stokes equations.uk_UA
dc.description.sponsorshipThe author thanks Athanasios Fokas for introducing him to this subject area. Also thanks for Chris Taylor and Euan Spence for many helpful discussions. This work is supported by an EPSRC studentship.uk_UA
dc.identifier.citationThe Fundamental k-Form and Global Relations / Anthony C.L. Ashton // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 5 назв. — англ.uk_UA
dc.identifier.issn1815-0659
dc.identifier.other2000 Mathematics Subject Classification: 30E25; 35E99; 35P05
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/148979
dc.language.isoenuk_UA
dc.publisherІнститут математики НАН Україниuk_UA
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlieruk_UA
dc.titleThe Fundamental k-Form and Global Relationsuk_UA
dc.typeArticleuk_UA

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