Time-periodic linear boundary value problems on a finite interval

A. S. Fokas; Beatrice Pelloni; David A. Smith

Time-periodic linear boundary value problems on a finite interval

A. S. Fokas, Beatrice Pelloni, David A. Smith

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Abstract

We study the large time behaviour of the solution of a linear dispersive PDEs posed on a finite interval, when the prescribed boundary conditions are time periodic. We use the approach pioneered in \cite{FL2012b} for nonlinear integrable PDEs. and then applied to linear problems on the half-line in \cite{fvdw2021}, to characterise necessary conditions for the solution of such a problem to be periodic, at least in an asymptotic sense. We then fully describe the periodicity properties of the solution in three important illustrative examples, recovering known results for the second-order cases and establishing new ones for the third order one.

Original language	English
Journal	Quarterly of Applied Mathematics
Publication status	Accepted/In press - 22 Jan 2022

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This is a pre-copyedited, author-produced version of an article accepted for publication in Quarterly of Applied Mathematics following peer review. The version of record will be available at: https://www.ams.org/publications/journals/journalsframework/qam
Accepted author manuscript, 2.46 MBLicence: CC BY-NC-ND

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title = "Time-periodic linear boundary value problems on a finite interval",

abstract = "We study the large time behaviour of the solution of a linear dispersive PDEs posed on a finite interval, when the prescribed boundary conditions are time periodic. We use the approach pioneered in \cite{FL2012b} for nonlinear integrable PDEs. and then applied to linear problems on the half-line in \cite{fvdw2021}, to characterise necessary conditions for the solution of such a problem to be periodic, at least in an asymptotic sense. We then fully describe the periodicity properties of the solution in three important illustrative examples, recovering known results for the second-order cases and establishing new ones for the third order one.",

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AU - Fokas, A. S.

AU - Pelloni, Beatrice

AU - Smith, David A.

PY - 2022/1/22

Y1 - 2022/1/22

N2 - We study the large time behaviour of the solution of a linear dispersive PDEs posed on a finite interval, when the prescribed boundary conditions are time periodic. We use the approach pioneered in \cite{FL2012b} for nonlinear integrable PDEs. and then applied to linear problems on the half-line in \cite{fvdw2021}, to characterise necessary conditions for the solution of such a problem to be periodic, at least in an asymptotic sense. We then fully describe the periodicity properties of the solution in three important illustrative examples, recovering known results for the second-order cases and establishing new ones for the third order one.

AB - We study the large time behaviour of the solution of a linear dispersive PDEs posed on a finite interval, when the prescribed boundary conditions are time periodic. We use the approach pioneered in \cite{FL2012b} for nonlinear integrable PDEs. and then applied to linear problems on the half-line in \cite{fvdw2021}, to characterise necessary conditions for the solution of such a problem to be periodic, at least in an asymptotic sense. We then fully describe the periodicity properties of the solution in three important illustrative examples, recovering known results for the second-order cases and establishing new ones for the third order one.

M3 - Article

SN - 0033-569X

JO - Quarterly of Applied Mathematics

JF - Quarterly of Applied Mathematics

ER -

Time-periodic linear boundary value problems on a finite interval

Abstract

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