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

Smith, D. A. (2012) Well-posed two-point initial-boundary value problems with arbitrary boundary conditions. Mathematical Proceedings of the Cambridge Philosophical Society, 152 (3). pp. 473-496. ISSN 1469-8064 doi: 10.1017/S030500411100082X

Abstract/Summary

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.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/26286
Identification Number/DOI	10.1017/S030500411100082X
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Cambridge University Press
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