Global attractor for a one dimensional weakly damped half-wave equation

Brahim Alouini

doi:10.3934/dcdss.2020410

Article Contents

2021, Volume 14, Issue 8: 2655-2670. Doi: 10.3934/dcdss.2020410

This issue Previous Article Non-standard boundary conditions for the linearized Korteweg-de Vries equation Next Article Lipschitz stability in determination of coefficients in a two-dimensional Boussinesq system by arbitrary boundary observation

Global attractor for a one dimensional weakly damped half-wave equation

Brahim Alouini

Laboratoire de Recherche: Analyse, Probabilité et Fractals, Faculté des Sciences de Monastir, Avenue de l'environnement, 5019 Monastir, Tunisie

Received: February 2020

Revised: April 2020

Early access: July 2020

Published: August 2021

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Abstract

We discuss the asymptotic behavior of the solutions for the fractional nonlinear Schrödinger equation that reads

$ u_t-iD u+ig(|u|^2)u+\gamma u = f\, . $

We prove that this behavior is characterized by the existence of a compact global attractor in the appropriate energy space.

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Mathematics Subject Classification: Primary: 35B40, 35Q55; Secondary: 76B03, 37L30.

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