On global solutions to the initial-boundary value problem for the damped nonlinear Schrödinger equations

DOI10.1016/0022-247X(90)90403-3zbMath0705.35131MaRDI QIDQ917811

Masayoshi Tsutsumi

Publication date: 1990

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

global existencedamping termsmall datadecay estimates

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (21)

Remarks on the damped nonlinear Schrödinger equation ⋮ Well-posedness and stability for Schrödinger equations with infinite memory ⋮ Solution of the forced nonlinear schrödinger (nls) equation using pde techniques ⋮ Stabilization of the weakly coupled Schrödinger system ⋮ A Note on a Damped Focusing Inhomogeneous Choquard Equation ⋮ Global existence and scattering for nonlinear Schrödinger equations with time-dependent damping ⋮ Long-time behavior for evolution processes associated with non-autonomous nonlinear Schrödinger equation ⋮ Uniform decay rates for the energy of weakly damped defocusing semilinear Schrödinger equations with inhomogeneous Dirichlet boundary control ⋮ Exponential stability for the nonlinear Schrödinger equation with locally distributed damping ⋮ Weakly-damped focusing nonlinear Schrödinger equations with Dirichlet control ⋮ Blow-up criteria for linearly damped nonlinear Schrödinger equations ⋮ Asymptotic behavior of the nonlinear damped Schrödinger equation ⋮ A note on the nonlinear Schrödinger equation in a general domain ⋮ Remarks on damped Schrödinger equation of Choquard type ⋮ 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 ⋮ Finite time extinction for the strongly damped nonlinear Schrödinger equation in bounded domains ⋮ Exponential stability for the locally damped defocusing Schrödinger equation on compact manifold ⋮ Damped non-linear coupled Schrödinger equations ⋮ Remarks on damped fractional Schrödinger equation with pure power nonlinearity

Cites Work

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• Global existence of small solutions to nonlinear evolution equations
• The initial value problem for the equations of motion of viscous and heat-conductive gases
• Dispersion of low-energy waves for two conservative equations
• Decay and asymptotics for \(\square u = F(u)\)
• Nonexistence of Global Solutions to the Cauchy Problem for the Damped Nonlinear Schrödinger Equations
• Nonlinear Schrödinger evolution equations
• Global, small amplitude solutions to nonlinear evolution equations

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