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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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