The Fundamental k-Form and Global Relations
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 coupl...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2008 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2008
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148979 |
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| Cite this: | 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. |
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Anthony C.L. Ashton 2019-02-19T12:24:52Z 2019-02-19T12:24:52Z 2008 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 https://nasplib.isofts.kiev.ua/handle/123456789/148979 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. The 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Fundamental k-Form and Global Relations Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
The Fundamental k-Form and Global Relations |
| spellingShingle |
The Fundamental k-Form and Global Relations Anthony C.L. Ashton |
| title_short |
The Fundamental k-Form and Global Relations |
| title_full |
The Fundamental k-Form and Global Relations |
| title_fullStr |
The Fundamental k-Form and Global Relations |
| title_full_unstemmed |
The Fundamental k-Form and Global Relations |
| title_sort |
fundamental k-form and global relations |
| author |
Anthony C.L. Ashton |
| author_facet |
Anthony C.L. Ashton |
| publishDate |
2008 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
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Інститут математики НАН України |
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Article |
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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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| issn |
1815-0659 |
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https://nasplib.isofts.kiev.ua/handle/123456789/148979 |
| citation_txt |
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. |
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AT anthonyclashton thefundamentalkformandglobalrelations AT anthonyclashton fundamentalkformandglobalrelations |
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2025-12-07T17:37:15Z |
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2025-12-07T17:37:15Z |
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1850871943143620608 |