scholarly journals Global solutions and self-similar solutions of the coupled system of semilinear wave equations in three space dimensions

2002 ◽  
Vol 9 (2) ◽  
pp. 471-482
Author(s):  
Kotaro Tsugawa ◽  
Hideo Kubo
Keyword(s):  
Wave Equations ◽  
Global Solutions ◽  
Coupled System ◽  
Semilinear Wave Equations ◽  
Self Similar ◽  
Similar Solutions ◽  
Three Space

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

2012 ◽  
Vol 09 (02) ◽  
pp. 263-323 ◽  
Author(s):  
SOICHIRO KATAYAMA
Keyword(s):  
Asymptotic Behavior ◽  
Global Existence ◽  
Small Amplitude ◽  
Wave Equations ◽  
Global Solutions ◽  
Small Data ◽  
Sufficient Condition ◽  
Null Condition ◽  
Semilinear Wave Equations ◽  
Three Space

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.

scholarly journals Self-similar solutions of semilinear wave equations with a focusing nonlinearity

Nonlinearity ◽  
2007 ◽  
Vol 20 (9) ◽  
pp. 2061-2074 ◽  
Author(s):  
Piotr Bizoń ◽  
Dieter Maison ◽  
Arthur Wasserman
Keyword(s):  
Wave Equations ◽  
Semilinear Wave Equations ◽  
Self Similar ◽  
Similar Solutions
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