Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 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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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: econ
1
The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph