## Well-posed boundary value problems for integrable evolution equations on a finite interval
Pelloni, B.
(2002)
Full text not archived in this repository. It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1023/A:1021163230712 ## Abstract/SummaryWe consider boundary value problems posed on an interval [0,L] for an arbitrary linear evolution equation in one space dimension with spatial derivatives of order n. We characterize a class of such problems that admit a unique solution and are well posed in this sense. Such well-posed boundary value problems are obtained by prescribing N conditions at x=0 and n–N conditions at x=L, where N depends on n and on the sign of the highest-degree coefficient n in the dispersion relation of the equation. For the problems in this class, we give a spectrally decomposed integral representation of the solution; moreover, we show that these are the only problems that admit such a representation. These results can be used to establish the well-posedness, at least locally in time, of some physically relevant nonlinear evolution equations in one space dimension.
Altmetric Deposit Details University Staff: Request a correction | Centaur Editors: Update this record |