scholarly journals Lecture notes : Global Well-posedness, scattering and blow up for the energy-critical, focusing, non-linear Schrödinger and wave equations

2007 ◽  
pp. 1-35 ◽  
Author(s):  
Carlos E. Kenig
Keyword(s):  
Wave Equations ◽  
Blow Up ◽  
Well Posedness ◽  
Non Linear ◽  
Lecture Notes

scholarly journals Blow up of negative initial-energy solutions of a system of nonlinear wave equations with variable-exponent nonlinearities

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Salim A. Messaoudi ◽  
Ala A. Talahmeh
Keyword(s):  
Nonlinear Wave ◽  
Variable Exponent ◽  
Wave Equations ◽  
Blow Up ◽  
Initial Energy ◽  
Nonlinear Wave Equations ◽  
Well Posedness

<p style='text-indent:20px;'>This work is concerned with a system of wave equations with variable-exponent nonlinearities acting in both equations. We, first, discuss the well-posedness then prove a blow up result for solutions with negative initial energy.</p>

Instability and Collapse in Discrete Wave Equations

2005 ◽  
Vol 5 (3) ◽  
pp. 223-241
Author(s):  
A. Carpio ◽  
G. Duro
Keyword(s):  
Continuum Limit ◽  
Wave Equations ◽  
Numerical Solutions ◽  
Blow Up ◽  
Theoretical Predictions ◽  
Initial States ◽  
The Impact ◽  
The Continuum

AbstractUnstable growth phenomena in spatially discrete wave equations are studied. We characterize sets of initial states leading to instability and collapse and obtain analytical predictions for the blow-up time. The theoretical predictions are con- trasted with the numerical solutions computed by a variety of schemes. The behavior of the systems in the continuum limit and the impact of discreteness and friction are discussed.

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