Global attractor for a nonlinear Schrödinger equation with a nonlinearity concentrated in one point

Wided Kechiche

doi:10.3934/dcdss.2021031

Article Contents

2021, Volume 14, Issue 8: 3027-3042. Doi: 10.3934/dcdss.2021031

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Global attractor for a nonlinear Schrödinger equation with a nonlinearity concentrated in one point

Wided Kechiche

Laboratoire de recherche: Analyse, Probabilité et Fractales, Faculté des Sciences de Monastir, Av. de l'environement, 5000 Monastir, Tunisie

Received: November 30, 2019

Revised: December 31, 2020

Early access: March 2021

Published: August 2021

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Abstract

We consider the nonlinear Schrödinger equation in dimension one with a nonlinearity concentrated in one point. We prove that this equation provides an infinite dimensional dynamical system. We also study the asymptotic behavior of the dynamics. We prove the existence of a global attractor for the system.

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Mathematics Subject Classification: Primary: 37L30, 37L50, 35Q55; Secondary: 35A01.

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