Well-posed boundary value problems for linear evolution equations on a finite interval
We identify the class of smooth boundary conditions that yield an initial-boundary value problem admitting a unique smooth solution for the case of a dispersive linear evolution PDE of arbitrary order, in one spatial dimension, defined on a finite interval. This result is obtained by an application...
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Published in | Mathematical proceedings of the Cambridge Philosophical Society Vol. 136; no. 2; pp. 361 - 382 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
Cambridge, UK
Cambridge University Press
01.03.2004
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Subjects | |
Online Access | Get full text |
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Summary: | We identify the class of smooth boundary conditions that yield an initial-boundary value problem admitting a unique smooth solution for the case of a dispersive linear evolution PDE of arbitrary order, in one spatial dimension, defined on a finite interval. This result is obtained by an application of a spectral transform method, introduced by Fokas, which allows us to reduce the problem to the study of the singularities of the set of functions arising as the unique solution of a certain linear system. |
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Bibliography: | istex:028D3557BE8DA080F37331B2CD0542FF114BF9C9 PII:S0305004103007205 ark:/67375/6GQ-5TV0JF5G-D |
ISSN: | 0305-0041 1469-8064 |
DOI: | 10.1017/S0305004103007205 |