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 Blow-Up of Solutions for Wave Equation Involving the Fractional Laplacian with Nonlinear Source

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Y. Bidi ◽  
A. Beniani ◽  
M. Y. Alnegga ◽  
A. Moumen
Keyword(s):  
Wave Equation ◽  
Fractional Laplacian ◽  
Blow Up ◽  
Nonlinear Source

In this paper, we study the blow-up of solutions for wave equation involving the fractional Laplacian with nonlinear source.

scholarly journals On asymptotic behavior of solution to a nonlinear wave equation with Space-time speed of propagation and damping terms

2021 ◽  
Vol 40 (6) ◽  
pp. 1615-1639
Author(s):  
Paul A. Ogbiyele ◽  
Peter O. Arawomo
Keyword(s):  
Asymptotic Behavior ◽  
Wave Equation ◽  
Space Time ◽  
Decay Estimates ◽  
Damped Wave Equation ◽  
Asymptotic Behavior Of Solution ◽  
Weighted Energy Method ◽  
Weighted Energy ◽  
Speed Of Propagation ◽  
Nonlinear Damped Wave Equation

In this paper, we consider the asymptotic behavior of solution to the nonlinear damped wave equation utt – div(a(t, x)∇u) + b(t, x)ut = −|u|p−1u t ∈ [0, ∞), x ∈ Rn u(0, x) = u0(x), ut(0, x) = u1(x) x ∈ Rn with space-time speed of propagation and damping potential. We obtained L2 decay estimates via the weighted energy method and under certain suitable assumptions on the functions a(t, x) and b(t, x). The technique follows that of Lin et al.[8] with modification to the region of consideration in Rn. These decay result extends the results in the literature.

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