Uniform decay rates for the energy of weakly damped defocusing semilinear Schrödinger equations with inhomogeneous Dirichlet boundary control

DOI10.1016/j.jde.2011.04.003zbMath1231.35238OpenAlexW2084882032MaRDI QIDQ639502

Türker Özsarı, Irena Lasiecka, Varga K. Kalantarov

Publication date: 22 September 2011

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2011.04.003

zbMATH Keywords

boundary controlexistencestabilizationnonlinear Schrödinger equationcompactnessmonotone operator theorydirect multiplier methodinhomogeneous Dirichlet boundary condition

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) NLS equations (nonlinear Schrödinger equations) (35Q55) Weak solutions to PDEs (35D30) Strong solutions to PDEs (35D35)

Related Items (22)

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 ⋮ Fractional Schrödinger equation; solvability and connection with classical Schrödinger equation ⋮ Exponential decay estimates for the damped defocusing Schrödinger equation in exterior domains ⋮ Optimal bilinear control of the logarithmic Schrödinger equation ⋮ Complex Ginzburg-Landau equations with dynamic boundary conditions ⋮ Exponential stability for the nonlinear Schrödinger equation with locally distributed damping ⋮ Stochastic nonlinear Schrödinger equation on an upper-right quarter plane with Dirichlet random boundary ⋮ Well-posedness for nonlinear Schrödinger equations with boundary forces in low dimensions by Strichartz estimates ⋮ Weakly-damped focusing nonlinear Schrödinger equations with Dirichlet control ⋮ Blow-up criteria for linearly damped nonlinear Schrödinger equations ⋮ Well-posedness and uniform decay rates for a nonlinear damped Schrödinger-type equation ⋮ Asymptotic behavior of cubic defocusing Schrödinger equations on compact surfaces ⋮ Inhomogeneous Dirichlet-boundary value problem for nonlinear Schrödinger equations with a power nonlinearity on the upper half-plane ⋮ Qualitative properties of solutions for nonlinear Schrödinger equations with nonlinear boundary conditions on the half-line ⋮ Exponential stability for a transmission problem of a nonlinear viscoelastic wave equation ⋮ 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 ⋮ Inhomogeneous Dirichlet boundary value problem for nonlinear Schrödinger equations in the upper half-space ⋮ INHOMOGENEOUS DIRICHLET-BOUNDARY VALUE PROBLEM FOR TWO-DIMENSIONAL QUADRATIC NONLINEAR SCHRÖDINGER EQUATIONS ⋮ Decay rate estimates for the wave equation with subcritical semilinearities and locally distributed nonlinear dissipation

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