scholarly journals On the lifespan and the blowup mechanism of smooth solutions to a class of 2-D nonlinear wave equations with small initial data

2015 ◽  
Vol 73 (4) ◽  
pp. 773-796 ◽  
Author(s):  
Ding Bingbing ◽  
Ingo Witt ◽  
Yin Huicheng
Keyword(s):  
Initial Data ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Nonlinear Wave Equations ◽  
Smooth Solutions ◽  
Small Initial Data

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.

scholarly journals Growth of Solutions with Positive Initial Energy to Systems of Nonlinear Wave Equations with Damping and Source Terms

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Erhan Pişkin
Keyword(s):  
Initial Data ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Initial Boundary ◽  
Initial Energy ◽  
Nonlinear Wave Equations ◽  
Source Terms ◽  
Positive Initial Energy ◽  
Damping And Source Terms ◽  
Growth Of Solutions

We consider initial-boundary conditions for coupled nonlinear wave equations with damping and source terms. We prove that the solutions of the problem are unbounded when the initial data are large enough in some sense.

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