scholarly journals Global attractors for strongly damped wave equations with displacement dependent damping and nonlinear source term of critical exponent

2011 ◽  
Vol 31 (1) ◽  
pp. 119-138 ◽  
Author(s):  
A. Kh. Khanmamedov ◽  
Keyword(s):  
Critical Exponent ◽  
Wave Equations ◽  
Source Term ◽  
Global Attractors ◽  
Nonlinear Source ◽  
Strongly Damped

scholarly journals The global attractors and dimensions estimation for the Kirchho type wave equations with nonlinear strongly damped terms

2016 ◽  
Vol 12 (3) ◽  
pp. 6087-6102
Author(s):  
Chengfei Ai ◽  
Huixian Zhu ◽  
Guoguang Lin
Keyword(s):  
Global Attractor ◽  
Wave Equations ◽  
Global Attractors ◽  
Time Behavior ◽  
Priori Estimate ◽  
Type Wave ◽  
Long Time ◽  
Uniqueness Of The Solution ◽  
The Galerkin Method ◽  
Strongly Damped

This paper studies the long time behavior of the solution to the initial boundaryvalue problems for a class of strongly damped Kirchho type wave equations:utt "1ut + j ut jp1 ut + j u jq1 u (kruk2)u = f(x):Firstly, we prove the existence and uniqueness of the solution by priori estimate and the Galerkin method. Then we obtain to the existence of the global attractor. Finally, we consider that the estimation of the upper bounds of Hausdor and fractal dimensionsfor the global attractor is obtained.

scholarly journals Quasi-stability and continuity of attractors for nonlinear system of wave equations

2021 ◽  
Vol 8 (1) ◽  
pp. 27-45
Author(s):  
M. M. Freitas ◽  
M. J. Dos Santos ◽  
A. J. A. Ramos ◽  
M. S. Vinhote ◽  
M. L. Santos
Keyword(s):  
Wave Equations ◽  
Coupled System ◽  
Global Attractors ◽  
Time Behavior ◽  
Exponential Attractors ◽  
Small Perturbations ◽  
Recent Approach ◽  
Nonlinear Coupled System ◽  
Long Time ◽  
External Forces

Abstract In this paper, we study the long-time behavior of a nonlinear coupled system of wave equations with damping terms and subjected to small perturbations of autonomous external forces. Using the recent approach by Chueshov and Lasiecka in [21], we prove that this dynamical system is quasi-stable by establishing a quasistability estimate, as consequence, the existence of global and exponential attractors is proved. Finally, we investigate the upper and lower semicontinuity of global attractors under autonomous perturbations.

Sign in / Sign up

Export Citation Format

Share Document