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Well-posed two-point initial-boundary value problems with arbitrary boundary conditions

Published online by Cambridge University Press:  12 December 2011

DAVID A. SMITH
DAVID A. SMITH*
Affiliation:
Department of Mathematics, University of ReadingRG6 6AX. e-mail: [email protected]
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Abstract

We study initial-boundary value problems for linear evolution equations of arbitrary spatial order, subject to arbitrary linear boundary conditions and posed on a rectangular 1-space, 1-time domain. We give a new characterisation of the boundary conditions that specify well-posed problems using Fokas' transform method. We also give a sufficient condition guaranteeing that the solution can be represented using a series.

The relevant condition, the analyticity at infinity of certain meromorphic functions within particular sectors, is significantly more concrete and easier to test than the previous criterion, based on the existence of admissible functions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 152 , Issue 3 , May 2012 , pp. 473 - 496
Copyright
Copyright © Cambridge Philosophical Society 2011

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References

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