The Fundamental k-Form and Global Relations

The Fundamental k-Form and Global Relations

Blog Article

In [Proc.Roy.Soc.London Ser.

A 453 (1997), no.1962, 1411-1443] Work Gloves 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 Table Accessory Set 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.