scholarly journals Global attractor of multi-valued operators with applications to a strongly damped nonlinear wave equation without uniqueness

2020 ◽  
Vol 25 (1) ◽  
pp. 223-240
Author(s):  
Zhiming Liu ◽  
◽  
Zhijian Yang
Keyword(s):  
Wave Equation ◽  
Global Attractor ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Strongly Damped

scholarly journals Global Attractor for Nonlinear Wave Equations with Critical Exponent on Unbounded Domain

2016 ◽  
Vol 1 (2) ◽  
pp. 581-602 ◽  
Author(s):  
Yuncheng You
Keyword(s):  
Wave Equation ◽  
Global Attractor ◽  
Nonlinear Wave ◽  
Unbounded Domain ◽  
Nonlinear Wave Equation ◽  
Wave Equations ◽  
Nonlinear Wave Equations ◽  
Growth Exponent ◽  
Global Dynamics ◽  
Dissipative Condition

AbstractAsymptotic and global dynamics of weak solutions for a damped nonlinear wave equation with a critical growth exponent on the unbounded domain ℝn(n ≥ 3) is investigated. The existence of a global attractor is proved under typical dissipative condition, which features the proof of asymptotic compactness of the solution semiflow in the energy space with critical nonlinear exponent by means of Vitali-type convergence theorem.

On the global existence and asymptotic behavior of the solution of a nonlinear wave equation with past history

2021 ◽  
Vol 62 (3) ◽  
pp. 031512
Author(s):  
Adel M. Al-Mahdi ◽  
Mohammad M. Al-Gharabli ◽  
Mohammad Kafini ◽  
Shadi Al-Omari
Keyword(s):  
Asymptotic Behavior ◽  
Wave Equation ◽  
Global Existence ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Past History
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