Long-time behavior of second order evolution equations with nonlinear damping

2008 ◽  
Vol 195 (912) ◽  
pp. 0-0 ◽  
Author(s):  
Igor Chueshov ◽  
Irena Lasiecka
Keyword(s):  
Evolution Equations ◽  
Nonlinear Damping ◽  
Second Order ◽  
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 $\begin{array}{} H^{1}_0({\it\Omega})\times L^{2}({\it\Omega})\times L^{2}_{\mu}(\mathbb{R}^{+};H^{1}_0({\it\Omega})) \end{array}$.

TIP INSTABILITY DURING CONFINED DIFFUSION-LIMITED GROWTH

1988 ◽  
Vol 02 (08) ◽  
pp. 945-951 ◽  
Author(s):  
DAVID A. KESSLER ◽  
HERBERT LEVINE
Keyword(s):  
Evolution Equations ◽  
Dynamical Behavior ◽  
Stable Steady State ◽  
Time Behavior ◽  
Two Dimensional ◽  
Long Time Behavior ◽  
Limited Growth ◽  
Channel Geometry ◽  
Diffusion Limited ◽  
Long Time

We study diffusion-limited crystal growth in a two dimensional channel geometry. We demonstrate that although there exists a linearly stable steady-state finger solution of the pattern evolution equations, the true dynamical behavior can be controlled by a tip-widening instability. Possible scenarios for the long-time behavior of the system are presented.

Dynamics for a plate equation with nonlinear damping on time-dependent space

2021 ◽  
pp. 1-17
Author(s):  
Penghui Zhang ◽  
Lu Yang
Keyword(s):  
Nonlinear Damping ◽  
Time Dependent ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Plate Equation ◽  
Long Time

In this paper, we study the long-time behavior of the following plate equation ε ( t ) u t t + g ( u t ) + Δ 2 u + λ u + f ( u ) = h , where the coefficient ε depends explicitly on time, the nonlinear damping and the nonlinearity both have critical growths.

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