The Long-Time Behavior of Solutions of a Nonlinear Fourth Order Wave Equation, Describing the Dynamics of Marine Risers

1997 ◽  
Vol 77 (3) ◽  
pp. 209-215 ◽  
Author(s):  
V. K. Kalantarov ◽  
A. Kurt
Keyword(s):  
Wave Equation ◽  
Fourth Order ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Marine Risers ◽  
Long Time ◽  
Fourth Order Wave Equation

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 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

scholarly journals Long-time behavior of solutions to a fourth-order nonlinear Schrödinger equation with critical nonlinearity

2021 ◽  
Author(s):  
Mamoru Okamoto ◽  
Kota Uriya
Keyword(s):  
Fourth Order ◽  
Decay Estimate ◽  
The Self ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Nls Equation ◽  
Nonlinear Schrödinger ◽  
Self Similar Solution ◽  
Long Time ◽  
Self Similar

AbstractWe consider the long-time behavior of solutions to a fourth-order nonlinear Schrödinger (NLS) equation with a derivative nonlinearity. By using the method of testing by wave packets, we construct an approximate solution and show that the solution for the fourth-order NLS has the same decay estimate for linear solutions. We prove that the self-similar solution is the leading part of the asymptotic behavior.

Sign in / Sign up

Export Citation Format

Share Document