The Fundamental k-Form and Global Relations
| dc.creator | Ashton, Anthony C. L. | |
| dc.date | 2007-11-29 | |
| dc.date | 2008-03-20 | |
| dc.date.accessioned | 2026-07-07T09:34:49Z | |
| dc.date.available | 2026-07-07T09:34:49Z | |
| dc.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. | |
| dc.description | Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/ | |
| dc.identifier | https://arxiv.org/abs/0711.4707 | |
| dc.identifier | http://arxiv.org/abs/0711.4707 | |
| dc.identifier | SIGMA 4 (2008), 033, 15 pages | |
| dc.identifier | doi:10.3842/SIGMA.2008.033 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159631 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Mathematical Physics | |
| dc.subject | 30E25 | |
| dc.title | The Fundamental k-Form and Global Relations | |
| dc.type | text |