scholarly journals The lifespan of solutions of semilinear wave equations with the scale-invariant damping in two space dimensions

2020 ◽  
Vol 269 (10) ◽  
pp. 8387-8424 ◽  
Author(s):  
Takuto Imai ◽  
Masakazu Kato ◽  
Hiroyuki Takamura ◽  
Kyouhei Wakasa
Keyword(s):  
Wave Equations ◽  
Scale Invariant ◽  
Semilinear Wave Equations ◽  
Two Space Dimensions

scholarly journals On Agemi-type structural conditions for a system of semilinear wave equations

2020 ◽  
Vol 17 (03) ◽  
pp. 459-473
Author(s):  
Yoshinori Nishii ◽  
Hideaki Sunagawa
Keyword(s):  
Small Amplitude ◽  
Wave Equations ◽  
Structural Condition ◽  
Two Component System ◽  
Component System ◽  
Semilinear Wave Equations ◽  
Two Component ◽  
Two Space Dimensions

We consider a two-component system of cubic semilinear wave equations in two space dimensions satisfying the Agemi-type structural condition (Ag) but violating (Ag0) and (Ag[Formula: see text]). For this system, we show that small amplitude solutions are asymptotically free as [Formula: see text].

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