Conformal conservation law, time decay and scattering for nonlinear wave equations

DOI10.1007/BF02788791zbMath1053.35104MaRDI QIDQ1880934

Kunio Hidano

Publication date: 27 September 2004

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

zbMATH Keywords

semilinear wave equationBesov space

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Second-order nonlinear hyperbolic equations (35L70) Initial value problems for second-order hyperbolic equations (35L15)

Related Items (9)

Analyticity of the scattering operator for semilinear dispersive equations ⋮ Bounded solutions to an energy subcritical non-linear wave equation on \(\mathbb{R}^3\) ⋮ Hörmander's method for the characteristic Cauchy problem and conformal scattering for a nonlinear wave equation ⋮ Long time behaviour of finite-energy radial solutions to energy subcritical wave equation in higher dimensions ⋮ Scattering theory for the subcritical wave equation with inverse square potential ⋮ Energy distribution of solutions to defocusing semi-linear wave equation in two dimensional space ⋮ Inward/outward energy theory of non-radial solutions to 3D semi-linear wave equation ⋮ A semi-linear shifted wave equation on the hyperbolic spaces with application on a quintic wave equation on $\mathbb {R}^2$ ⋮ Energy distribution of radial solutions to energy subcritical wave equation with an application on scattering theory

Cites Work

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• Nonlinear small data scattering for the wave and Klein-Gordon equation
• The global Cauchy problem for the nonlinear Klein-Gordon equation
• Scattering theory in the energy space for a class of nonlinear wave equations
• The scattering theory for the nonlinear wave equation with small data
• The scattering theory for the nonlinear wave equation with small data. II
• Nonlinear scattering theory at low energy
• Decay of solutions of nonlinear wave equations in three space dimensions
• Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
• Scattering and self-similar solutions for the nonlinear wave equation
• On existence and scattering with minimal regularity for semilinear wave equations
• Generalized Strichartz inequalities for the wave equation
• Decay and asymptotics for \(\square u = F(u)\)
• The global Goursat problem and scattering for nonlinear wave equations
• The decay of solutions of the exterior initial-boundary value problem for the wave equation
• Uniform decay estimates and the lorentz invariance of the classical wave equation
• Life–span of classocal solutions to fully nonlinear wave equations
• Remarks on the global sobolev inequalities in the minkowski space Rⁿ⁺¹
• Endpoint Strichartz estimates
• Unique global existence and asymptotic behaviour of solutions for wave equations with non-coercive critical nonlinearity
• A note on the life-span of classical solutions to nonlinear wave equations in four space dimensions
• The limiting amplitude principle
• Scattering problem for the nonlinear wave equation in the finite energy and conformal charge space

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