Title :

Finite dimensional global attractor for a semi-discrete fractional nonlinear Schrödinger equation

Author(s) :

Calgaro, Caterina [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Reliable numerical approximations of dissipative systems [RAPSODI]
Goubet, Olivier [Auteur]
Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352 UPJV [LAMFA]
Zahrouni, Ezzeddine [Auteur]

Journal title :

Mathematical Methods in the Applied Sciences

Publisher :

Wiley

Publication date :

2017

ISSN :

0170-4214

English keyword(s) :

fractal dimension
Nonlinear Schrödinger equations
Crank-Nicolson scheme
global attractor

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]

English abstract : [en]

We consider a semi-discrete in time Crank-Nicolson scheme to discretise a weakly damped forced nonlinear fractional Schrödinger equation u t − i(−∆) α u + i|u| 2 u + γu = f for α ∈ (1 2 , 1) considered in the the whole ...
Show more >We consider a semi-discrete in time Crank-Nicolson scheme to discretise a weakly damped forced nonlinear fractional Schrödinger equation u t − i(−∆) α u + i|u| 2 u + γu = f for α ∈ (1 2 , 1) considered in the the whole space R. We prove that such semi-discrete equation provides a discrete infinite dimensional dynamical in H α (R) that possesses a global attractor in H α (R). We show also that if the external force is in a suitable weighted Lebesgue space then this global attractor has a finite fractal dimension.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL