Global existence and open loop exponential stabilization of weak solutions for nonlinear Schrödinger equations with localized external Neumann manipulation

DOI10.1016/J.NA.2012.10.006zbMath1260.35210OpenAlexW2016798905MaRDI QIDQ1937584

Türker Özsarı

Publication date: 1 March 2013

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2012.10.006

zbMATH Keywords

compactness methodstabilizationglobal existenceGalerkin's methodnonlinear Schrödinger equationslong time behaviorinhomogeneous Neumann boundary data

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) NLS equations (nonlinear Schrödinger equations) (35Q55) Weak solutions to PDEs (35D30)

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The interior-boundary Strichartz estimate for the Schrödinger equation on the half-line revisited ⋮ Well-posedness and stability for Schrödinger equations with infinite memory ⋮ Stabilization of the weakly coupled Schrödinger system ⋮ Complex Ginzburg-Landau equations with dynamic boundary conditions ⋮ Exponential stability for the nonlinear Schrödinger equation with locally distributed damping ⋮ Well-posedness for nonlinear Schrödinger equations with boundary forces in low dimensions by Strichartz estimates ⋮ Blow-up criteria for linearly damped nonlinear Schrödinger equations ⋮ Qualitative properties of solutions for nonlinear Schrödinger equations with nonlinear boundary conditions on the half-line ⋮ Well-posedness and energy decay estimates in the Cauchy problem for the damped defocusing Schrödinger equation

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