Long time behavior for damped generalized coupled nonlinear wave equations. II. Unbounded domain

2001 ◽  
Vol 6 (2) ◽  
pp. 107-110 ◽  
Author(s):  
Shaomei Fang ◽  
Boling Guo
Keyword(s):  
Nonlinear Wave ◽  
Unbounded Domain ◽  
Wave Equations ◽  
Nonlinear Wave Equations ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Long Time

scholarly journals Time-dependent attractor of wave equations with nonlinear damping and linear memory

2019 ◽  
Vol 17 (1) ◽  
pp. 89-103
Author(s):  
Qiaozhen Ma ◽  
Jing Wang ◽  
Tingting Liu
Keyword(s):  
Wave Equation ◽  
Wave Equations ◽  
Nonlinear Damping ◽  
Time Dependent ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Long Time

Abstract In this article, we consider the long-time behavior of solutions for the wave equation with nonlinear damping and linear memory. Within the theory of process on time-dependent spaces, we verify the process is asymptotically compact by using the contractive functions method, and then obtain the existence of the time-dependent attractor in $\begin{array}{} H^{1}_0({\it\Omega})\times L^{2}({\it\Omega})\times L^{2}_{\mu}(\mathbb{R}^{+};H^{1}_0({\it\Omega})) \end{array}$.

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.

scholarly journals Long-time behavior for fourth-order wave equations with strain term and nonlinear weak damping term

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Chao Yang ◽  
Yanbing Yang
Keyword(s):  
Asymptotic Behavior ◽  
Fourth Order ◽  
Wave Equations ◽  
Source Term ◽  
Nonlinear Wave Equations ◽  
Time Behavior ◽  
Damping Term ◽  
Long Time ◽  
The Relationship ◽  
Weak Damping

<p style='text-indent:20px;'>We mainly focus on the asymptotic behavior analysis for certain fourth-order nonlinear wave equations with strain term, nonlinear weak damping term and source term. We establish two theorems on the asymptotic behavior of the solution depending on some conditions related to the relationship among the forced strain term, the nonlinear weak damping term and source terms.</p>

Long-time behavior of solutions for a system of N-coupled nonlinear dissipative half-wave equations

Analysis ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Brahim Alouini
Keyword(s):  
Asymptotic Behavior ◽  
Initial Value Problem ◽  
Wave Equations ◽  
Well Posedness ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Initial Value ◽  
Half Wave ◽  
Long Time ◽  
Asymptotic Dynamics

Abstract In the current paper, we consider a system of N-coupled weakly dissipative fractional nonlinear Schrödinger equations. The well-posedness of the initial value problem is established by a refined analysis based on a limiting argument as well as the study of the asymptotic dynamics of the solutions. This asymptotic behavior is described by the existence of a compact global attractor in the appropriate energy space.

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