Asymptotic Stability for the Damped Schrödinger Equation on Noncompact Riemannian Manifolds and Exterior Domains

DOI10.1080/03605302.2014.908390zbMath1302.58008OpenAlexW2000186570MaRDI QIDQ2926046

Marcelo Moreira Cavalcanti, César Augusto Bortot

Publication date: 29 October 2014

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605302.2014.908390

zbMATH Keywords

exponential stabilitySchrödinger equationnon-compact manifolds

Mathematics Subject Classification ID

Elliptic equations on manifolds, general theory (58J05) Schrödinger operator, Schrödinger equation (35J10)

Related Items (12)

Local energy decay and smoothing effect for the damped Schrödinger equation ⋮ Well-posedness and stability for Schrödinger equations with infinite memory ⋮ Exponential decay for the coupled Klein-Gordon-Schrödinger equations with locally distributed damping ⋮ Exponential decay estimates for the damped defocusing Schrödinger equation in exterior domains ⋮ Asymptotic behavior of the coupled Klein–Gordon–Schrödinger systems on compact manifolds ⋮ 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 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 ⋮ 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

Cites Work

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• Sobolev spaces on Riemannian manifolds
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• Uniform decay rate estimates for Schrödinger and plate equations with nonlinear locally distributed damping
• Smoothing Effect for the Regularized Schrödinger Equation with Non-Controlled Orbits
• Stabilization of Schrödinger equation in exterior domains
• Solutions of the wave equation with localized energy

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