scholarly journals $ L^p $-$ L^q $ estimates for the damped wave equation and the critical exponent for the nonlinear problem with slowly decaying data

2019 ◽  
Vol 18 (4) ◽  
pp. 1967-2008 ◽  
Author(s):  
Masahiro Ikeda ◽  
◽  
Takahisa Inui ◽  
Mamoru Okamoto ◽  
Yuta Wakasugi ◽  
...  
Keyword(s):  
Wave Equation ◽  
Critical Exponent ◽  
Nonlinear Problem ◽  
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.

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