scholarly journals Cauchy problem for quasi-linear wave equations with nonlinear damping and source terms

2004 ◽  
Vol 300 (1) ◽  
pp. 218-243 ◽  
Author(s):  
Zhijian Yang
Keyword(s):  
Cauchy Problem ◽  
Wave Equations ◽  
Nonlinear Damping ◽  
Linear Wave ◽  
Source Terms ◽  
Linear Wave Equations ◽  
Damping And Source Terms

Global Existence and Asymptotic Behavior of Solutions for Nonlinear Wave Equations

2014 ◽  
Vol 490-491 ◽  
pp. 327-330
Author(s):  
Ji Bing Zhang ◽  
Yun Zhu Gao
Keyword(s):  
Asymptotic Behavior ◽  
Global Existence ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Nonlinear Damping ◽  
Nonlinear Wave Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Potential Well ◽  
Source Terms ◽  
Damping And Source Terms

In this paper, we concern with the nonlinear wave equations with nonlinear damping and source terms. By using the potential well method, we obtain a result for the global existence and asymptotic behavior of the solutions.

scholarly journals Global Nonexistence of Positive Initial-Energy Solutions for Coupled Nonlinear Wave Equations with Damping and Source Terms

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Liang Fei ◽  
Gao Hongjun
Keyword(s):  
Nonlinear Wave ◽  
Wave Equations ◽  
Nonlinear Damping ◽  
Initial Energy ◽  
Nonlinear Wave Equations ◽  
Source Terms ◽  
Nonexistence Theorem ◽  
Positive Initial Energy ◽  
Global Nonexistence ◽  
Damping And Source Terms

This work is concerned with a system of nonlinear wave equations with nonlinear damping and source terms acting on both equations. We prove a global nonexistence theorem for certain solutions with positive initial energy.

scholarly journals SOLUTIONS OF QUASI-LINEAR WAVE EQUATIONS POLYHOMOGENEOUS AT NULL INFINITY IN HIGH DIMENSIONS

2011 ◽  
Vol 08 (02) ◽  
pp. 269-346 ◽  
Author(s):  
PIOTR T. CHRUŚCIEL ◽  
ROGER TAGNE WAFO
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Maxwell Equations ◽  
Wave Equations ◽  
Hyperbolic Systems ◽  
Small Data ◽  
Linear Wave ◽  
High Dimensions ◽  
Null Infinity ◽  
Linear Wave Equations

We prove propagation of weighted Sobolev regularity for solutions of the hyperboloidal Cauchy problem for a class of quasi-linear symmetric hyperbolic systems, under structure conditions compatible with the Einstein–Maxwell equations in space-time dimensions n + 1 ≥ 7. Similarly we prove propagation of polyhomogeneity in dimensions n + 1 ≥ 9. As a byproduct we obtain, in those last dimensions, polyhomogeneity at null infinity of small data solutions of vacuum Einstein, or Einstein–Maxwell equations evolving out of initial data which are stationary outside of a ball.

Non-existence of global solutions for a class of wave equations with nonlinear damping and source terms

2011 ◽  
Vol 141 (4) ◽  
pp. 865-880 ◽  
Author(s):  
Shun-Tang Wu
Keyword(s):  
Wave Equations ◽  
Global Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlinear Damping ◽  
Critical Value ◽  
Initial Energy ◽  
Source Terms ◽  
Initial Boundary Value ◽  
Damping And Source Terms

An initial–boundary-value problem for a class of wave equations with nonlinear damping and source terms in a bounded domain is considered. We establish the non-existence result of global solutions with the initial energy controlled above by a critical value via the method introduced in a work by Autuori et al. in 2010. This improves the 2009 result of Liu and Wang.

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