Existence of global attractor for one-dimensional weakly damped nonlinear Schrödinger equation with Dirac interaction and artificial boundary condition in half-line

Abstract We consider a nonlinear Schrödinger equation with Dirac interaction defect. Moreover, non-standard boundary conditions are introduced in connection to the behavior of the solutions. First, we prove that this kind of Schrödinger equation can be characterized by an autonomous dynamical system...

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Main Authors:	Mostafa Abounouh, Hassan Al Moatassime, Abderrazak Chrifi
Format:	Article
Language:	English
Published:	SpringerOpen 2017-05-01
Series:	Advances in Difference Equations
Subjects:	damped nonlinear Schrödinger equation Dirac interaction defect artificial boundary condition autonomous dynamical system global attractor
Online Access:	http://link.springer.com/article/10.1186/s13662-017-1194-2

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spelling	doaj-0822280ff3ae469cadf0895178a14d2d2020-11-24T20:43:05ZengSpringerOpenAdvances in Difference Equations1687-18472017-05-012017112410.1186/s13662-017-1194-2Existence of global attractor for one-dimensional weakly damped nonlinear Schrödinger equation with Dirac interaction and artificial boundary condition in half-lineMostafa Abounouh0Hassan Al Moatassime1Abderrazak Chrifi2Department of Mathematics, Faculty of Science and Technology, Cadi Ayyad UniversityDepartment of Mathematics, Faculty of Science and Technology, Cadi Ayyad UniversityDepartment of Mathematics, Faculty of Science and Technology, Cadi Ayyad UniversityAbstract We consider a nonlinear Schrödinger equation with Dirac interaction defect. Moreover, non-standard boundary conditions are introduced in connection to the behavior of the solutions. First, we prove that this kind of Schrödinger equation can be characterized by an autonomous dynamical system. Then, based on this result, we show that such an equation possesses a maximal compact attractor in the weak topology of H 1 $\mathbf{H}^{\mathbf{1}}$ .http://link.springer.com/article/10.1186/s13662-017-1194-2damped nonlinear Schrödinger equationDirac interaction defectartificial boundary conditionautonomous dynamical systemglobal attractor
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Mostafa Abounouh Hassan Al Moatassime Abderrazak Chrifi
spellingShingle	Mostafa Abounouh Hassan Al Moatassime Abderrazak Chrifi Existence of global attractor for one-dimensional weakly damped nonlinear Schrödinger equation with Dirac interaction and artificial boundary condition in half-line Advances in Difference Equations damped nonlinear Schrödinger equation Dirac interaction defect artificial boundary condition autonomous dynamical system global attractor
author_facet	Mostafa Abounouh Hassan Al Moatassime Abderrazak Chrifi
author_sort	Mostafa Abounouh
title	Existence of global attractor for one-dimensional weakly damped nonlinear Schrödinger equation with Dirac interaction and artificial boundary condition in half-line
title_short	Existence of global attractor for one-dimensional weakly damped nonlinear Schrödinger equation with Dirac interaction and artificial boundary condition in half-line
title_full	Existence of global attractor for one-dimensional weakly damped nonlinear Schrödinger equation with Dirac interaction and artificial boundary condition in half-line
title_fullStr	Existence of global attractor for one-dimensional weakly damped nonlinear Schrödinger equation with Dirac interaction and artificial boundary condition in half-line
title_full_unstemmed	Existence of global attractor for one-dimensional weakly damped nonlinear Schrödinger equation with Dirac interaction and artificial boundary condition in half-line
title_sort	existence of global attractor for one-dimensional weakly damped nonlinear schrödinger equation with dirac interaction and artificial boundary condition in half-line
publisher	SpringerOpen
series	Advances in Difference Equations
issn	1687-1847
publishDate	2017-05-01
description	Abstract We consider a nonlinear Schrödinger equation with Dirac interaction defect. Moreover, non-standard boundary conditions are introduced in connection to the behavior of the solutions. First, we prove that this kind of Schrödinger equation can be characterized by an autonomous dynamical system. Then, based on this result, we show that such an equation possesses a maximal compact attractor in the weak topology of H 1 $\mathbf{H}^{\mathbf{1}}$ .
topic	damped nonlinear Schrödinger equation Dirac interaction defect artificial boundary condition autonomous dynamical system global attractor
url	http://link.springer.com/article/10.1186/s13662-017-1194-2
work_keys_str_mv	AT mostafaabounouh existenceofglobalattractorforonedimensionalweaklydampednonlinearschrodingerequationwithdiracinteractionandartificialboundaryconditioninhalfline AT hassanalmoatassime existenceofglobalattractorforonedimensionalweaklydampednonlinearschrodingerequationwithdiracinteractionandartificialboundaryconditioninhalfline AT abderrazakchrifi existenceofglobalattractorforonedimensionalweaklydampednonlinearschrodingerequationwithdiracinteractionandartificialboundaryconditioninhalfline
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Existence of global attractor for one-dimensional weakly damped nonlinear Schrödinger equation with Dirac interaction and artificial boundary condition in half-line

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