Conformal conservation law, time decay and scattering for nonlinear wave equations
type: Item
instance of: scholarly article
title: Conformal conservation law, time decay and scattering for nonlinear wave equations
zbMATH Open document ID: 1053.35104
DOI: 10.1007/BF02788791
author: Kunio Hidano
published in: Journal d'Analyse Mathématique
publication date: 2004-09-27T00:00:00Z
review text: The author considers solutions of the Cauchy problem to the equation \[ u_{tt}-\triangle u+\lambda _1| u| ^{\rho _1-1}u+\lambda _2| u| ^{\rho _2-1}u=0, \qquad t\in \mathbb{R}, \;x\in \mathbb{R}^n\;(n=3\dots 7). \] He improves results of \textit{J. Ginibre} and \textit{G. Velo} [Ann. Inst. Henri Poincaré, Phys. Théor. 47, 221--261, 263--276 (1987; Zbl 0644.35067)] and deduces sharp estimates for asymptotic behavior of the solution to the problem.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35L15
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 2103498
zbMATH Keywords: semilinear wave equation
zbMATH Keywords: Besov space
reviewed by: Marie Kopáčková
MaRDI profile type: Publication
cites work: The global Goursat problem and scattering for nonlinear wave equations
cites work: Q4112938
cites work: Q4309703
cites work: The global Cauchy problem for the nonlinear Klein-Gordon equation
cites work: Q3786846
cites work: Scattering theory in the energy space for a class of nonlinear wave equations
cites work: Generalized Strichartz inequalities for the wave equation
cites work: Q3772629
cites work: Q4824303
cites work: Scattering problem for the nonlinear wave equation in the finite energy and conformal charge space
cites work: Scattering and self-similar solutions for the nonlinear wave equation
cites work: Endpoint Strichartz estimates
cites work: Uniform decay estimates and the lorentz invariance of the classical wave equation
cites work: Remarks on the global sobolev inequalities in the minkowski space Rn+1
cites work: Life–span of classocal solutions to fully nonlinear wave equations
cites work: A note on the life-span of classical solutions to nonlinear wave equations in four space dimensions
cites work: On existence and scattering with minimal regularity for semilinear wave equations
cites work: The scattering theory for the nonlinear wave equation with small data
cites work: The scattering theory for the nonlinear wave equation with small data. II
cites work: The decay of solutions of the exterior initial-boundary value problem for the wave equation
cites work: The limiting amplitude principle
cites work: Unique global existence and asymptotic behaviour of solutions for wave equations with non-coercive critical nonlinearity
cites work: Decay of solutions of nonlinear wave equations in three space dimensions
cites work: Nonlinear small data scattering for the wave and Klein-Gordon equation
cites work: Q4317280
cites work: Q5475904
cites work: Decay and asymptotics for \(\square u = F(u)\)
cites work: Nonlinear scattering theory at low energy
cites work: Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
cites work: Q4858785
description: scientific article; zbMATH DE number 2103498