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

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  • 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.

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

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    [2] M. Abounouh, H. Al Moatassime and A. 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, 2017 (2017), 137. doi: 10.1186/s13662-017-1194-2.
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