scientific article

zbMath0634.35059MaRDI QIDQ3772629

Yoshio Isutsumi, Nakao Hayashi

Publication date: 1987

Full work available at URL: http://www.numdam.org/item?id=AIHPA_1987__46_2_187_0

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zbMATH Keywords

scattering theoryasymptotic completenesswave operatorsscattering statesasymptotic behavior in timeHartree type equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Scattering theory for PDEs (35P25)

Related Items (29)

Unnamed Item ⋮ On the focusing generalized Hartree equation ⋮ Conformal conservation law, time decay and scattering for nonlinear wave equations ⋮ Energy-critical Hartree equation with harmonic potential for radial data ⋮ On small data scattering of Hartree equations with short-range interaction ⋮ Short-range scattering of Hartree type fractional NLS ⋮ Global behavior of solutions to the focusing generalized Hartree equation ⋮ The inverse scattering problem for Schrödinger and Klein-Gordon equations with a nonlocal nonlinearity ⋮ On the Cauchy problem for the Hartree type semilinear Schrödinger equation in the de Sitter spacetime ⋮ Global well-posedness for the defocusing Hartree equation with radial data in ℝ4 ⋮ Modified scattering operator for the Hartree-Fock equation ⋮ H m -modified wave operator for nonlinear Hartree equation in space of dimensionn≥2 ⋮ Sharp threshold of global existence for a nonlocal nonlinear Schrödinger system in \(\mathbb{R}^3\) ⋮ Inverse scattering problems for the Hartree equation whose interaction potential decays rapidly ⋮ The Cauchy problem for the Hartree equations under random influences ⋮ Global well-posedness and scattering for the energy-critical, defocusing Hartree equation for radial data ⋮ Asymptotic expansion of the solution to the nonlinear Schrödinger equation with nonlocal interaction ⋮ On the analytic smoothing effect for the Hartree equation with a short range interaction potential ⋮ Long range scattering and modified wave operators for some Hartree type equations. III: Gevrey spaces and low dimensions ⋮ Global well-posedness and scattering for the defocusing Hartree equation in \(\mathbb R^3\) ⋮ Long-range scattering for time-dependent Hartree-Fock type equation ⋮ Sharp conditions of global existence for nonlinear Schrödinger and Klein-Gordon equations. ⋮ Scattering problem for the nonlinear wave equation in the finite energy and conformal charge space ⋮ Global well-posedness and scattering for the defocusing \(H^{\frac 1 2}\)-subcritical Hartree equation in \(\mathbb R^d\) ⋮ Lower bounds for order of decay or of growth in time for solutions to linear and nonlinear Schrödinger equations ⋮ Smoothing effect for some Schrödinger equations ⋮ Scattering theory for semilinear Schrödinger equations with an inverse-square potential via energy methods ⋮ Dispersive estimates for nonlinear Schrödinger equations with external potentials ⋮ Uniqueness in the inverse scattering problem for Hartree type equation

Cites Work

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