The Fundamental k-Form and Global Relations
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
The Fundamental k-Form and Global Relations
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| Creator |
Anthony C.L. Ashton
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| Description |
In [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.
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| Date |
2019-02-19T12:24:52Z
2019-02-19T12:24:52Z 2008 |
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| Type |
Article
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| Identifier |
The Fundamental k-Form and Global Relations / Anthony C.L. Ashton // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 5 назв. — англ.
1815-0659 2000 Mathematics Subject Classification: 30E25; 35E99; 35P05 http://dspace.nbuv.gov.ua/handle/123456789/148979 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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