Global existence and stability for semilinear wave equations damped by time-dependent boundary frictions

2019 ◽  
Vol 354 ◽  
pp. 282-295 ◽  
Author(s):  
Zhe Jiao ◽  
Yong Xu
Keyword(s):  
Global Existence ◽  
Wave Equations ◽  
Time Dependent ◽  
Semilinear Wave Equations ◽  
Existence And Stability

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.

A Modified Test Function Method for Damped Wave Equations

2013 ◽  
Vol 13 (4) ◽  
Author(s):  
Marcello D’Abbicco ◽  
Sandra Lucente
Keyword(s):  
Wave Equation ◽  
Global Existence ◽  
Critical Exponent ◽  
Function Method ◽  
Wave Equations ◽  
Time Dependent ◽  
Small Data ◽  
Test Function ◽  
Test Function Method ◽  
Modified Test

AbstractIn this paper we use a modified test function method to derive nonexistence results for the semilinear wave equation with time-dependent speed and damping. The obtained critical exponent is the same exponent of some recent results on global existence of small data solutions.

scholarly journals Weighted Strichartz estimates and global existence for semilinear wave equations

1997 ◽  
Vol 119 (6) ◽  
pp. 1291-1319 ◽  
Author(s):  
Vladimir Georgiev ◽  
Hans Lindblad ◽  
Christopher Donald Sogge
Keyword(s):  
Global Existence ◽  
Wave Equations ◽  
Strichartz Estimates ◽  
Semilinear Wave Equations
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