Long-time behavior of a Bose-Einstein equation in a two-dimensional thin domain

Brahim Alouini

doi:10.3934/cpaa.2011.10.1629

Article Contents

2011, Volume 10, Issue 6: 1629-1643. Doi: 10.3934/cpaa.2011.10.1629

This issue Previous Article A generalization of $H$-measures and application on purely fractional scalar conservation laws Next Article Solutions of a pure critical exponent problem involving the half-laplacian in annular-shaped domains

Long-time behavior of a Bose-Einstein equation in a two-dimensional thin domain

Brahim Alouini^1,

1.
Unité de recherche: Ondelettes et Fractals, Faculté des Sciences de Monastir, Av. de l'environnement, 5000 Monastir

Received: February 28, 2010

Revised: October 31, 2010

Published: October 2011

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Abstract

We study the long-time behavior of the solutions to a nonlinear Schrödinger equation with a zero order dissipation and a quadratic potential when they are driven by an external force on a thin canal. We show that this behavior is described by a regular attractor which captures all the trajectories and have a finite Fractal dimension.

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Mathematics Subject Classification: Primary: 35L05, 35Q55; Secondary: 76B03.

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