The Fundamental k-Form and Global Relations

Details The Fundamental k-Form and Global Relations The Fundamental k-Form and Global Relations

2007-11-29

arxiv.org/abs/0711.4707v3

SIGMA 4 (2008), 033, 15 pages

Mathematics

Analysis of PDEs

Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

Scientific paper

10.3842/SIGMA.2008.033

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.

Affiliated with

Also associated with

No associations

Rating

The Fundamental k-Form and Global Relations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Fundamental k-Form and Global Relations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Fundamental k-Form and Global Relations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-45981