scholarly journals Pointwise long time behavior for the mixed damped nonlinear wave equation in \mathbb{R}^n_+

2020 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Linglong Du ◽  
◽  
Min Yang ◽  
Keyword(s):  
Wave Equation ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
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 Long time stability of KAM tori for nonlinear wave equation

2015 ◽  
Vol 258 (8) ◽  
pp. 2823-2846 ◽  
Author(s):  
Hongzi Cong ◽  
Meina Gao ◽  
Jianjun Liu
Keyword(s):  
Wave Equation ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Kam Tori ◽  
Time Stability ◽  
Long Time ◽  
Long Time Stability

Global Well-Posedness for the Defocusing, Cubic, Nonlinear Wave Equation in Three Dimensions for Radial Initial Data in .H s × .H s-1, s> 1/2

2018 ◽  
Vol 2019 (21) ◽  
pp. 6797-6817
Author(s):  
Benjamin Dodson
Keyword(s):  
Wave Equation ◽  
Initial Data ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Three Dimensions ◽  
Well Posedness ◽  
Critical Space ◽  
Initial Value ◽  
Long Time ◽  
Well Posed

Abstract In this paper we study the defocusing, cubic nonlinear wave equation in three dimensions with radial initial data. The critical space is $\dot{H}^{1/2} \times \dot{H}^{-1/2}$. We show that if the initial data is radial and lies in $\left (\dot{H}^{s} \times \dot{H}^{s - 1}\right ) \cap \left (\dot{H}^{1/2} \times \dot{H}^{-1/2}\right )$ for some $s> \frac{1}{2}$, then the cubic initial value problem is globally well-posed. The proof utilizes the I-method, long time Strichartz estimates, and local energy decay. This method is quite similar to the method used in [11].

scholarly journals Long Time Behavior for a Wave Equation with Time Delay

2017 ◽  
Vol 21 (1) ◽  
pp. 107-129 ◽  
Author(s):  
Gongwei Liu ◽  
Hongyun Yue ◽  
Hongwei Zhang
Keyword(s):  
Wave Equation ◽  
Time Delay ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Long Time

scholarly journals Long-time behavior of a semilinear wave equation with memory

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Baowei Feng ◽  
Maurício L Pelicer ◽  
Doherty Andrade
Keyword(s):  
Wave Equation ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Semilinear Wave Equation ◽  
Long Time ◽  
With Memory
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