ASYMPTOTIC POINTWISE BEHAVIOR FOR SYSTEMS OF SEMILINEAR WAVE EQUATIONS IN THREE SPACE DIMENSIONS

Soichiro Katayama

Type: Article

Publication Date: 2012-06-01

Citations: 14

DOI: https://doi.org/10.1142/s0219891612500099

Abstract

In connection with the weak null condition, Alinhac introduced a sufficient condition for global existence of small amplitude solutions to systems of semilinear wave equations in three space dimensions. We introduce a slightly weaker sufficient condition for the small data global existence, and we investigate the asymptotic pointwise behavior of global solutions for systems satisfying this condition. As an application, the asymptotic behavior of global solutions under the Alinhac condition is also derived.

Locations

Journal of Hyperbolic Differential Equations - View
arXiv (Cornell University) - View - PDF
DataCite API - View

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Global existence and asymptotic behavior of solutions to systems of semilinear wave equations in two space dimensions	2008	Soichiro Katayama
+	Remarks on the asymptotic behavior of global solutions to systems of semilinear wave equations	2019	Soichiro Katayama
+	Asymptotic behavior of solutions to semilinear systems of wave equations	2008	Soichiro Katayama Hideo Kubo
+	Global stability of solutions to nonlinear wave equations	2012	Shiwu Yang
+	Global existence and the asymptotic behavior for systems of nonlinear wave equations violating the null condition	2020	Soichiro Katayama
+	ON THE LARGE TIME BEHAVIOR OF SOLUTIONS TO SEMILINEAR SYSTEMS OF THE WAVE EQUATION	2009	Soichiro Katayama H. Kubo
+ PDF Chat	On the Global Behavior of Weak Null Quasilinear Wave Equations	2019	Yu Deng Fabio Pusateri
+	Small Data Blowup for Systems of Semilinear Wave Equations with Different Propagation Speeds in Three Space Dimensions	2000	Hideo Kubo Masahito Ohta
+	Global solutions of quasilinear wave equations	2005	Hans Lindblad
+	Global and almost global existence for general quasilinear wave equations in two space dimensions	2018	Dongbing Zha
+	Small data solutions of 3-D quasilinear wave equations under null condition	2018	Yingbo Liu
+	On the global behavior of weak null quasilinear wave equations	2018	Yu Deng Fabio Pusateri
+	Asymptotic behavior of global solutions to some systems of semilinear wave equations	2008	Soichiro Katayama
+	Almost global existence for semilinear wave equations with mixed nonlinearities in four space dimensions	2017	Chengbo Wang Hao Zhou
+ PDF Chat	Global existence for systems of nonlinear wave and Klein–Gordon equations in two space dimensions under a kind of the weak null condition	2022	Minggang Cheng
+	Semilinear hyperbolic systems violating the null condition	2012	Soichiro Katayama Toshiaki Matoba Hideaki Sunagawa
+	On Conditions of Global Existence for Systems of Quasilinear Wave Equations in Three Space Dimensions	1998	和義横山
+	On Conditions of Global Existence for Systems of Quasilinear Wave Equations in Three Space Dimensions	1998	Kazuyoshi Yokoyama
+	Global solutions and the asymptotic behavior for nonlinear wave equations with small initial data	2017	聡一郎片山
+	Global Existence Theorem for Semilinear Wave Equations with Non-compact Data in Two Space Dimensions	1993	Kimitoshi Tsutaya

Works That Cite This (18)

Action	Title	Year	Authors
+ PDF Chat	The Role of Metrics in the Theory of Partial Differential Equations	2020
+	The global nonlinear stability of Minkowski space for self-gravitating massive fields	2015	Philippe G. LeFloch Yue Ma
+ PDF Chat	The hyperboloidal foliation method for nonlinear wave equations	2015	Philippe G. LeFloch Yue Ma
+	On the global behavior of weak null quasilinear wave equations	2018	Yu Deng Fabio Pusateri
+ PDF Chat	The global nonlinear stability of Minkowski spacetime for self-gravitating massive fields. A brief overview	2016	Philippe G. LeFloch
+	The global nonlinear stability of Minkowski space for self-gravitating massive fields	2015	Philippe G. LeFloch Yue Ma
+	Asymptotic behavior for systems of nonlinear wave equations with multiple propagation speeds in three space dimensions	2013	Soichiro Katayama
+ PDF Chat	Global Evolution of the U(1) Higgs Boson: Nonlinear Stability and Uniform Energy Bounds	2020	Shijie Dong Philippe G. LeFloch Zoe Wyatt
+ PDF Chat	Asymptotic behavior for a class of derivative nonlinear Schrödinger systems	2020	Soichiro Katayama Daisuke Sakoda
+ PDF Chat	The Global Nonlinear Stability of Minkowski Space for Self-gravitating Massive Fields	2016	Philippe G. LeFloch Yue Ma

Works Cited by This (22)

Action	Title	Year	Authors
+	Large time asymptotics of solutions to nonlinear Klein-Gordon systems	2005	Hideaki Sunagawa
+	The lifespan of classical solutions of non-linear hyperbolic equations	1987	Lars Hörmander
+ PDF Chat	A note on the large time asymptotics for a system of Klein-Gordon equations	2004	Hideaki Sunagawa
+	Semilinear hyperbolic systems with blowup at infinity	2006	Serge Alinhac
+	Existence of a global solution to a semi–linear wave equation with slowly decreasing initial data in three space dimensions	1986	Fumioki Asakura
+	Blow‐up for quasi‐linear wave equations in three space dimensions	1981	Fritz John
+	On the lifespan of solutions of nonlinear wave equations with small initial data	1990	Hans Lindblad
+	Existence for large times of strict solutions of nonlinear wave equations in three space dimensions for small initial data	1987	Fritz John
+	Uniform decay estimates and the lorentz invariance of the classical wave equation	1985	Sergiù Klainerman
+ PDF Chat	The weak null condition for Einstein's equations	2003	Hans Lindblad Igor Rodnianski