Existence for large times of strict solutions of nonlinear wave equations in three space dimensions for small initial data

1987 ◽  
Vol 40 (1) ◽  
pp. 79-109 ◽  
Author(s):  
Fritz John
Keyword(s):  
Initial Data ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Nonlinear Wave Equations ◽  
Small Initial Data ◽  
Strict Solutions ◽  
Three Space

THE LIFESPAN OF SOLUTIONS OF EXTERIOR RADIAL QUASILINEAR CAUCHY–NEUMANN PROBLEMS

2008 ◽  
Vol 05 (03) ◽  
pp. 519-546 ◽  
Author(s):  
PAUL GODIN
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Wave Equations ◽  
Smooth Solutions ◽  
Small Initial Data ◽  
Precise Information ◽  
Neumann Problems ◽  
Quasilinear Wave Equations ◽  
Three Space

We consider smooth solutions of radial exterior Cauchy–Neumann problems with small initial data for radial quasilinear wave equations in three space dimensions, when the size of the initial data tends to 0. We obtain rather precise information on the lifespan, analogous with well known Cauchy problem results of Hörmander and John.

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