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

BEATRICE PELLONI

doi:10.1017/S0305004103007205

Abstract

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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.

Crossref Citations

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

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