Title :

Asymptotics of linear initial boundary value problems with periodic boundary data on the half-line and finite intervals

Author(s) :

Dujardin, Guillaume [Auteur]
SImulations and Modeling for PArticles and Fluids [SIMPAF]

Journal title :

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Pages :

3341-3360

Publisher :

Royal Society, The

Publication date :

2009-11-01

ISSN :

1364-5021

HAL domain(s) :

Mathématiques [math]/Analyse classique [math.CA]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Systèmes dynamiques [math.DS]
Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [en]

This paper deals with the asymptotic behaviour of the solutions of linear initial boundary value problems with constant coefficients on the half-line and on finite intervals. We assume that the boundary data are periodic ...
Show more >This paper deals with the asymptotic behaviour of the solutions of linear initial boundary value problems with constant coefficients on the half-line and on finite intervals. We assume that the boundary data are periodic in time and we investigate whether the solution becomes time-periodic after sufficiently long time. Using the Fokas' transformation method, we show that for the linear Schrödinger equation, the linear heat equation and the linearised KdV equation on the half-line, the solutions indeed become periodic for large time. However, for the same linear Schr\"pdinger equation on a finite interval, we show that the solution, in general, is not asymptotically periodic; actually, the asymptotic behaviour of the solution depends on the commensurability of the time period T of the boundary data with the square of the length of the interval over π.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL