scholarly journals Long-time dynamics of Kirchhoff wave models with strong nonlinear damping

2012 ◽  
Vol 252 (2) ◽  
pp. 1229-1262 ◽  
Author(s):  
Igor Chueshov
Keyword(s):  
Nonlinear Damping ◽  
Time Dynamics ◽  
Long Time ◽  
Wave Models ◽  
Long Time Dynamics

scholarly journals Long-time dynamics for a class of extensible beams with nonlocal nonlinear damping*

2017 ◽  
Vol 6 (3) ◽  
pp. 437-470 ◽  
Author(s):  
Marcio Antonio Jorge da Silva ◽  
◽  
Vando Narciso ◽  
Keyword(s):  
Nonlinear Damping ◽  
Time Dynamics ◽  
Long Time ◽  
Nonlocal Nonlinear ◽  
Long Time Dynamics

scholarly journals Existence and continuity of global attractors for ternary mixtures of solids

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Mirelson M. Freitas ◽  
Anderson J. A. Ramos ◽  
Baowei Feng ◽  
Mauro L. Santos ◽  
Helen C. M. Rodrigues
Keyword(s):  
Global Attractors ◽  
Nonlinear Damping ◽  
Ternary Mixtures ◽  
Small Perturbations ◽  
Time Dynamics ◽  
The Family ◽  
Long Time ◽  
Finite Fractal Dimension ◽  
Dense Set ◽  
Long Time Dynamics

<p style='text-indent:20px;'>In this paper, we study the long-time dynamics of a system modelinga mixture of three interacting continua with nonlinear damping, sources terms and subjected to small perturbations of autonomousexternal forces with a parameter <inline-formula><tex-math id="M1">\begin{document}$ \epsilon $\end{document}</tex-math></inline-formula>, inspired by the modelstudied by Dell' Oro and Rivera [<xref ref-type="bibr" rid="b12">12</xref>]. We establish astabilizability estimate for the associated gradient dynamicalsystem, which as a consequence, implies the existence of a compactglobal attractor with finite fractal dimension andexponential attractors. This estimate is establishedindependent of the parameter <inline-formula><tex-math id="M2">\begin{document}$ \epsilon\in[0,1] $\end{document}</tex-math></inline-formula>. We also prove thesmoothness of global attractors independent of the parameter<inline-formula><tex-math id="M3">\begin{document}$ \epsilon\in[0,1] $\end{document}</tex-math></inline-formula>. Moreover, we show that the family of globalattractors is continuous with respect to the parameter <inline-formula><tex-math id="M4">\begin{document}$ \epsilon $\end{document}</tex-math></inline-formula> ona residual dense set <inline-formula><tex-math id="M5">\begin{document}$ I_*\subset[0,1] $\end{document}</tex-math></inline-formula> in the same sense proposed inHoang et al. [<xref ref-type="bibr" rid="b15">15</xref>].</p>

Long-time dynamics of a nonlinear Timoshenko beam with discrete delay term and nonlinear damping

2020 ◽  
Vol 61 (6) ◽  
pp. 061505
Author(s):  
M. J. Dos Santos ◽  
M. M. Freitas ◽  
A. J. A. Ramos ◽  
D. S. Almeida Júnior ◽  
L. R. S. Rodrigues
Keyword(s):  
Timoshenko Beam ◽  
Nonlinear Damping ◽  
Discrete Delay ◽  
Time Dynamics ◽  
Delay Term ◽  
Long Time ◽  
Long Time Dynamics

Long-time dynamics of a class of nonlocal extensible beams with time delay

2021 ◽  
pp. 108128652110194
Author(s):  
Fengjuan Meng ◽  
Cuncai Liu ◽  
Chang Zhang
Keyword(s):  
Time Delay ◽  
Stability Property ◽  
Beam Equation ◽  
Exponential Attractors ◽  
Time Dynamics ◽  
Bounded Smooth Domain ◽  
Finite Dimensional ◽  
Long Time ◽  
Bounded Smooth ◽  
Long Time Dynamics

This work is devoted to the following nonlocal extensible beam equation with time delay: [Formula: see text] on a bounded smooth domain [Formula: see text]. The main purpose of this paper is to consider the long-time dynamics of the system. Under suitable assumptions, the quasi-stability property of the system is established, based on which the existence and regularity of a finite-dimensional compact global attractor are obtained. Moreover, the existence of exponential attractors is proved.

scholarly journals Singular Limit and Long-Time Dynamics of Bresse Systems

2017 ◽  
Vol 49 (4) ◽  
pp. 2468-2495 ◽  
Author(s):  
To Fu Ma ◽  
Rodrigo Nunes Monteiro
Keyword(s):  
Singular Limit ◽  
Time Dynamics ◽  
Long Time ◽  
Long Time Dynamics

Long-time dynamics via direct summation of infinite continued fractions

1992 ◽  
Vol 68 (11) ◽  
pp. 1637-1640 ◽  
Author(s):  
Zhi-Xiong Cai ◽  
Surajit Sen ◽  
S. D. Mahanti
Keyword(s):  
Continued Fractions ◽  
Time Dynamics ◽  
Long Time ◽  
Long Time Dynamics ◽  
Direct Summation
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