Global attractor for an extensible beam equation with localized nonlinear damping and linear memory

2011 ◽  
Vol 34 (12) ◽  
pp. 1430-1439 ◽  
Author(s):  
Jum-Ran Kang
Keyword(s):  
Global Attractor ◽  
Nonlinear Damping ◽  
Beam Equation

scholarly journals Strong Attractor of Beam Equation with Structural Damping and Nonlinear Damping

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Danxia Wang ◽  
Jianwen Zhang ◽  
Yinzhu Wang
Keyword(s):  
Phase Space ◽  
Global Attractor ◽  
Continuous Semigroup ◽  
Nonlinear Damping ◽  
Beam Equation ◽  
Structural Damping ◽  
Asymptotic Compactness

This paper is mainly concerned with the existence of a global strong attractor for the nonlinear extensible beam equation with structural damping and nonlinear external damping. This kind of problem arises from the model of an extensible vibration beam. By the asymptotic compactness of the related continuous semigroup, we prove the existence of a strong global attractor which is connected with phase spaceD(Δ2)×H01(Ω)∩H2(Ω).

scholarly journals Global Attractors of the Extensible Plate Equations with Nonlinear Damping and Memory

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Xiaobin Yao ◽  
Qiaozhen Ma
Keyword(s):  
Global Attractor ◽  
Function Method ◽  
Global Attractors ◽  
Nonlinear Damping ◽  
Kirchhoff Type ◽  
Contraction Function ◽  
Plate Equations

We prove in this paper the existence of a global attractor for the plate equations of Kirchhoff type with nonlinear damping and memory using the contraction function method.

scholarly journals Stochastic dynamic for an extensible beam equation with localized nonlinear damping and linear memory

2020 ◽  
Vol 4 (1) ◽  
pp. 400-416
Author(s):  
Abdelmajid Ali Dafallah ◽  
◽  
Fadlallah Mustafa Mosa ◽  
Mohamed Y. A. Bakhet ◽  
Eshag Mohamed Ahmed ◽  
...  
Keyword(s):  
Nonlinear Damping ◽  
Random Attractor ◽  
Beam Equation ◽  
Stochastic Dynamic ◽  
Uniqueness Of Solutions ◽  
Stochastic Dynamical System ◽  
Autonomous Case ◽  
Bounded Absorbing Set ◽  
Linear Damping ◽  
Longtime Behavior

In this paper, we concerned to prove the existence of a random attractor for the stochastic dynamical system generated by the extensible beam equation with localized non-linear damping and linear memory defined on bounded domain. First we investigate the existence and uniqueness of solutions, bounded absorbing set, then the asymptotic compactness. Longtime behavior of solutions is analyzed. In particular, in the non-autonomous case, the existence of a random attractor attractors for solutions is achieved.

Uniform decay rate estimates for the beam equation with locally distributed nonlinear damping

2021 ◽  
Author(s):  
Marcelo M. Cavalcanti ◽  
Leonel G. Delatorre ◽  
Valéria N. Domingos Cavalcanti ◽  
Victor H. Gonzalez Martinez ◽  
Daiane C. Soares
Keyword(s):  
Decay Rate ◽  
Nonlinear Damping ◽  
Beam Equation ◽  
Uniform Decay

scholarly journals Existence, decay and blow up of solutions for the extensible beam equation with nonlinear damping and source terms

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Erhan Pişkin
Keyword(s):  
Contraction Mapping ◽  
Blow Up ◽  
Nonlinear Damping ◽  
Contraction Mapping Principle ◽  
Beam Equation ◽  
Source Terms ◽  
Banach Contraction ◽  
Damping And Source Terms ◽  
Banach Contraction Mapping Principle ◽  
Banach Contraction Mapping

AbstractWe consider the existence, both locally and globally in time, the decay and the blow up of the solution for the extensible beam equation with nonlinear damping and source terms. We prove the existence of the solution by Banach contraction mapping principle. The decay estimates of the solution are proved by using Nakao’s inequality. Moreover, under suitable conditions on the initial datum, we prove that the solution blow up in finite time.

Sign in / Sign up

Export Citation Format

Share Document