Well-posedness and energy decay estimates for the damped wave equation with lrlocalizing coefficient

1998 ◽  
Vol 23 (9-10) ◽  
pp. 1839-1855 ◽  
Author(s):  
Louis Roder Tcheugoué Tébou ◽  
Louis Roder Tcheugoué Tébou
Keyword(s):  
Wave Equation ◽  
Energy Decay ◽  
Well Posedness ◽  
Decay Estimates ◽  
Damped Wave Equation

scholarly journals Global existence and dynamic structure of solutions for damped wave equation involving the fractional Laplacian

2021 ◽  
Vol 54 (1) ◽  
pp. 245-258
Author(s):  
Younes Bidi ◽  
Abderrahmane Beniani ◽  
Khaled Zennir ◽  
Ahmed Himadan
Keyword(s):  
Wave Equation ◽  
Global Solution ◽  
Fractional Laplacian ◽  
Necessary Conditions ◽  
Dynamic Structure ◽  
Decay Estimates ◽  
Damped Wave Equation ◽  
Structure Of Solutions ◽  
Nonlinear Source ◽  
Galerkin Approximations

Abstract We consider strong damped wave equation involving the fractional Laplacian with nonlinear source. The results of global solution under necessary conditions on the critical exponent are established. The existence is proved by using the Galerkin approximations combined with the potential well theory. Moreover, we showed new decay estimates of global solution.

scholarly journals Energy decay for the damped wave equation on an unbounded network

2018 ◽  
Vol 7 (3) ◽  
pp. 335-351
Author(s):  
Rachid Assel ◽  
◽  
Mohamed Ghazel
Keyword(s):  
Wave Equation ◽  
Energy Decay ◽  
Damped Wave Equation

scholarly journals Local energy decay for the damped wave equation

2014 ◽  
Vol 266 (7) ◽  
pp. 4538-4615 ◽  
Author(s):  
Jean-Marc Bouclet ◽  
Julien Royer
Keyword(s):  
Wave Equation ◽  
Energy Decay ◽  
Local Energy ◽  
Damped Wave Equation

scholarly journals Scattering for critical wave equations with variable coefficients

2021 ◽  
pp. 1-19
Author(s):  
Shi-Zhuo Looi ◽  
Mihai Tohaneanu
Keyword(s):  
Wave Equation ◽  
Wave Equations ◽  
Variable Coefficients ◽  
Energy Decay ◽  
Time Dependent ◽  
Linear Wave ◽  
Decay Estimates ◽  
Local Energy ◽  
Linear Wave Equation ◽  
Semilinear Wave Equation

Abstract We prove that solutions to the quintic semilinear wave equation with variable coefficients in ${{\mathbb {R}}}^{1+3}$ scatter to a solution to the corresponding linear wave equation. The coefficients are small and decay as $|x|\to \infty$ , but are allowed to be time dependent. The proof uses local energy decay estimates to establish the decay of the $L^{6}$ norm of the solution as $t\to \infty$ .

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