Well-posed boundary value problems for linear evolution equations on a finite interval

Beatrice Pelloni

doi:10.1017/S0305004103007205

Well-posed boundary value problems for linear evolution equations on a finite interval

Beatrice Pelloni

School of Mathematical & Computer Sciences

Research output: Contribution to journal › Article › peer-review

33 Citations (Scopus)

Abstract

We identify the class of smooth boundary conditions that yield an initial-boundaryvalue problem admitting a unique smooth solution for the case of a dispersive linearevolution PDE of arbitrary order, in one spatial dimension, defined on a finiteinterval.This result is obtained by an application of a spectral transform method, introducedby Fokas, which allows us to reduce the problem to the study of the singularitiesof the set of functions arising as the unique solution of a certain linearsystem.

Original language	English
Pages (from-to)	361-382
Number of pages	22
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	136
Issue number	2
DOIs	https://doi.org/10.1017/S0305004103007205
Publication status	Published - Mar 2004

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abstract = "We identify the class of smooth boundary conditions that yield an initial-boundaryvalue problem admitting a unique smooth solution for the case of a dispersive linearevolution PDE of arbitrary order, in one spatial dimension, defined on a finiteinterval.This result is obtained by an application of a spectral transform method, introducedby Fokas, which allows us to reduce the problem to the study of the singularitiesof the set of functions arising as the unique solution of a certain linearsystem.",

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AB - We identify the class of smooth boundary conditions that yield an initial-boundaryvalue problem admitting a unique smooth solution for the case of a dispersive linearevolution PDE of arbitrary order, in one spatial dimension, defined on a finiteinterval.This result is obtained by an application of a spectral transform method, introducedby Fokas, which allows us to reduce the problem to the study of the singularitiesof the set of functions arising as the unique solution of a certain linearsystem.

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Well-posed boundary value problems for linear evolution equations on a finite interval

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