Scattering theory for the wave equation of a Hartree type in three space dimensions

DOI10.3934/DCDS.2014.34.2261zbMath1276.35123OpenAlexW2330401141MaRDI QIDQ379873

Kimitoshi Tsutaya

Publication date: 11 November 2013

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2014.34.2261

zbMATH Keywords

wave equationscattering problemHartree type

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Second-order nonlinear hyperbolic equations (35L70) Wave equation (35L05)

Related Items (3)

Initial boundary value problem for a class of wave equations of Hartree type ⋮ Unnamed Item ⋮ Global Cauchy problems for the Klein-Gordon, wave and fractional Schr\"odinger equations with Hartree nonlinearity on modulation spaces

Cites Work

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• On the asymptotic behavior of nonlinear waves in the presence of a short-range potential
• Weighted estimates for a convolution appearing in the wave equation of Hartree type
• On small data scattering with cubic convolution nonlinearity
• Scattering for semilinear wave equations with small data in three space dimensions
• On a wave equation with a cubic convolution
• Blow-up of solutions of nonlinear wave equations in three space dimensions
• Existence and blow up of small amplitude nonlinear waves with a negative potential
• Existence and blow up of small-amplitude nonlinear waves with a sign-changing potential
• Stability and intersection properties of solutions to the nonlinear biharmonic equation
• Existence of a global solution to a semi–linear wave equation with slowly decreasing initial data in three space dimensions

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