Exponential stability for the \(2\)-D defocusing Schrödinger equation with locally distributed damping.

zbMath1240.35509MaRDI QIDQ637018

Marcelo Moreira Cavalcanti, Fábio M. Amorin Natali, Ryuichi Fukuoka, Valéria Neves Domingos Cavalcanti

Publication date: 1 September 2011

Published in: Differential and Integral Equations (Search for Journal in Brave)

zbMATH Keywords

exponential stabilityunique continuation propertylocally distributed damping\(2\)-D defocusing Schrödinger equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) NLS equations (nonlinear Schrödinger equations) (35Q55) Continuation and prolongation of solutions to PDEs (35B60)

Related Items (13)

Remarks on the damped nonlinear Schrödinger equation ⋮ Well-posedness and stability for Schrödinger equations with infinite memory ⋮ Exponential decay estimates for the damped defocusing Schrödinger equation in exterior domains ⋮ Decay of solutions to damped Korteweg-de Vries type equation ⋮ Exponential stability for the nonlinear Schrödinger equation with locally distributed damping ⋮ Well-posedness and uniform decay rates for a nonlinear damped Schrödinger-type equation ⋮ Asymptotic behavior of cubic defocusing Schrödinger equations on compact surfaces ⋮ Qualitative aspects for the cubic nonlinear Schrödinger equations with localized damping: exponential and polynomial stabilization ⋮ Exponential stability of the nonlinear Schrödinger equation with locally distributed damping on compact Riemannian manifold ⋮ Well-posedness and energy decay estimates in the Cauchy problem for the damped defocusing Schrödinger equation ⋮ Well-posedness and asymptotic behavior of a generalized higher order nonlinear Schrödinger equation with localized dissipation ⋮ Exponential stability for the locally damped defocusing Schrödinger equation on compact manifold ⋮ Exponential stabilization for the nonlinear Schrödinger equation with localized damping

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