Galerkin method of weakly damped cubic nonlinear Schrödinger with Dirac impurity, and artificial boundary condition in a half-line

Abderrazak Chrifi; Mostafa Abounouh; Hassan Al Moatassime

doi:10.3934/dcdss.2021030

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2022, Volume 15, Issue 1: 79-93. Doi: 10.3934/dcdss.2021030

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Galerkin method of weakly damped cubic nonlinear Schrödinger with Dirac impurity, and artificial boundary condition in a half-line

Department of Mathematics, Faculty of Science and Technology, Cadi Ayyad University, B.P. 549, Av. Abdelkarim Elkhattabi, Guéliz, Marrakesh, 40000, Morocco

^* Corresponding author: Abderrazak Chrifi (abderrazak.chrifi@gmail.com)
^* Corresponding author: Abderrazak Chrifi (abderrazak.chrifi@gmail.com)

Received: July 31, 2020

Revised: December 31, 2020

Early access: March 2021

Published: January 2022

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Abstract

We consider a weakly damped cubic nonlinear Schrödinger equation with Dirac interaction defect in a half line of $ \mathbb{R} $. Endowed with artificial boundary condition at the point $ x = 0 $, we discuss the global existence and uniqueness of solution of this equation by using Faedo–Galerkin method.

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Mathematics Subject Classification: Primary: 35Q55, 49K40; Secondary: 37L65.

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