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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Bibliographic Details
Published inMathematical proceedings of the Cambridge Philosophical Society Vol. 136; no. 2; pp. 361 - 382
Main Author PELLONI, BEATRICE
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.03.2004
Subjects
Boundary value problems
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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.
Bibliography:istex:028D3557BE8DA080F37331B2CD0542FF114BF9C9
PII:S0305004103007205
ark:/67375/6GQ-5TV0JF5G-D
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004103007205