# American Institute of Mathematical Sciences

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)

Received  August 2020 Revised  January 2021 Early access March 2021

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.

Citation: Abderrazak Chrifi, Mostafa Abounouh, Hassan Al Moatassime. Galerkin method of weakly damped cubic nonlinear Schrödinger with Dirac impurity, and artificial boundary condition in a half-line. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2021030
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