Stable and unstable sets for damped nonlinear wave equations with variable exponent sources

2021 ◽  
Vol 62 (1) ◽  
pp. 011507
Author(s):  
Le Cong Nhan ◽  
Le Xuan Truong
Keyword(s):  
Nonlinear Wave ◽  
Variable Exponent ◽  
Wave Equations ◽  
Nonlinear Wave Equations ◽  
Stable And Unstable Sets

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>

scholarly journals A uniqueness result for the Sine-Gordon breather

2021 ◽  
Vol 2 (2) ◽  
Author(s):  
Rainer Mandel
Keyword(s):  
Nonlinear Wave ◽  
Wave Equations ◽  
Uniqueness Result ◽  
Nonlinear Wave Equations

AbstractIn this note we prove that the sine-Gordon breather is the only quasimonochromatic breather in the context of nonlinear wave equations in $$\mathbb {R}^N$$ R N .

scholarly journals Global existence and decay estimates for nonlinear wave equations with space-time dependent dissipative term

2015 ◽  
Vol 12 (02) ◽  
pp. 249-276
Author(s):  
Tomonari Watanabe
Keyword(s):  
Global Existence ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Space Time ◽  
Time Dependent ◽  
Nonlinear Wave Equations ◽  
Energy Estimates ◽  
Space Region ◽  
Decay Estimates ◽  
Dissipative Term

We study the global existence and the derivation of decay estimates for nonlinear wave equations with a space-time dependent dissipative term posed in an exterior domain. The linear dissipative effect may vanish in a compact space region and, moreover, the nonlinear terms need not be in a divergence form. In order to establish higher-order energy estimates, we introduce an argument based on a suitable rescaling. The proposed method is useful to control certain derivatives of the dissipation coefficient.

Derivation of nonlinear wave equations for ultrasound beam in nonuniform bubbly liquids

2012 ◽  
Author(s):  
Tetsuya Kanagawa ◽  
Takeru Yano ◽  
Junya Kawahara ◽  
Kazumichi Kobayashi ◽  
Masao Watanabe ◽  
...  
Keyword(s):  
Nonlinear Wave ◽  
Wave Equations ◽  
Nonlinear Wave Equations ◽  
Ultrasound Beam ◽  
Bubbly Liquids
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