Finite dimensional global attractor for a damped fractional anisotropic Schrödinger type equation with harmonic potential

Brahim Alouini

doi:10.3934/cpaa.2020206

Article Contents

2020, Volume 19, Issue 9: 4545-4573. Doi: 10.3934/cpaa.2020206

This issue Previous Article Motion of interfaces for a damped hyperbolic Allen–Cahn equation Next Article Optimal decay to the non-isentropic compressible micropolar fluids

Finite dimensional global attractor for a damped fractional anisotropic Schrödinger type equation with harmonic potential

Brahim Alouini

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

Received: January 2020

Revised: March 2020

Published: June 2020

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Abstract

We study the long time behaviour of the solutions for a class of nonlinear damped fractional Schrödinger type equation with anisotropic dispersion and in presence of a quadratic potential in a two dimensional unbounded domain. We prove that this behaviour is characterized by the existence of regular compact global attractor with finite fractal dimension.

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Mathematics Subject Classification: Primary: 35B40, 35Q55, 35B41; Secondary: 76B03, 37L30.

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