Exponential attractors for weakly damped wave equation with sub-quintic nonlinearity

2019 ◽  
Vol 78 (3) ◽  
pp. 1026-1036 ◽  
Author(s):  
Fengjuan Meng ◽  
Cuncai Liu
Keyword(s):  
Wave Equation ◽  
Damped Wave Equation ◽  
Exponential Attractors ◽  
Quintic Nonlinearity

scholarly journals Strong Exponential Attractors for Weakly Damped Semilinear Wave Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Cuncai Liu ◽  
Fengjuan Meng ◽  
Chang Zhang
Keyword(s):  
Wave Equation ◽  
Wave Equations ◽  
Strichartz Estimate ◽  
Exponential Attractor ◽  
Damped Wave Equation ◽  
Exponential Attractors ◽  
Bounded Smooth Domain ◽  
Strong Energy ◽  
Bounded Smooth ◽  
Recent Extension

In this paper, we investigate the longtime dynamics for the damped wave equation in a bounded smooth domain of ℝ3. The exponential attractor is investigated in a strong energy space for the case of subquintic nonlinearity, which is based on the recent extension of the Strichartz estimate for the case of a bounded domain. The results obtained complete some previous works.

scholarly journals Uniform exponential attractors for a singularly perturbed damped wave equation

2003 ◽  
Vol 10 (1-2) ◽  
pp. 211-238 ◽  
Author(s):  
Pierre Fabrie ◽  
Cedric Galusinski ◽  
A. Miranville ◽  
Sergey Zelik
Keyword(s):  
Wave Equation ◽  
Singularly Perturbed ◽  
Damped Wave Equation ◽  
Exponential Attractors

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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