scholarly journals Strong Solutions and Global Attractors for Kirchhoff Type Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Xiangping Chen
Keyword(s):  
Phase Space ◽  
Type Equation ◽  
Strong Solutions ◽  
Global Attractors ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Kirchhoff Type ◽  
Kirchhoff Type Equation ◽  
Long Time ◽  
Linear Damping

We study the long-time behavior of the Kirchhoff type equation with linear damping. We prove the existence of strong solution and the semigroup associated with the solution possesses a global attractor in the higher phase space.

scholarly journals Upper Semicontinuous Property of Uniform Attractors for the 2D Nonautonomous Navier-Stokes Equations with Damping

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Xin-Guang Yang ◽  
Jun-Tao Li
Keyword(s):  
External Force ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Navier Stokes Equations ◽  
Upper Semicontinuous ◽  
Long Time ◽  
Linear Damping ◽  
Uniform Attractors

Our aim is to investigate the long-time behavior in terms of upper semicontinuous property of uniform attractors for the 2D nonautonomous Navier-Stokes equations with linear damping and nonautonomous perturbation external force, that is, the convergence of corresponding attractors when the perturbation tends to zero.

Global Attractors for p-Laplacian Equations with Dynamic Flux Boundary Conditions

2013 ◽  
Vol 13 (2) ◽  
Author(s):  
Bo You ◽  
Chengkui Zhong
Keyword(s):  
Boundary Conditions ◽  
Polynomial Growth ◽  
Arbitrary Order ◽  
Global Attractors ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Flux Boundary Conditions ◽  
Long Time ◽  
Bounded Smooth ◽  
Laplacian Equations

AbstractThis paper studies the long-time behavior of solutions for p-Laplacian equations with a polynomial growth nonlinearity of arbitrary order and dynamic flux boundary conditions in d-dimensional bounded smooth domains. We first prove the existence of global attractors in L

scholarly journals Pullback𝒟-Attractor of Nonautonomous Three-Component Reversible Gray-Scott System on Unbounded Domains

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Anhui Gu
Keyword(s):  
Phase Space ◽  
Global Attractor ◽  
Unbounded Domains ◽  
Time Behavior ◽  
External Forcing ◽  
Long Time Behavior ◽  
Entire Space ◽  
Asymptotic Compactness ◽  
Uniform Estimates ◽  
Long Time

The long time behavior of solutions of the nonautonomous three-components reversible Gray-Scott system defined on the entire spaceℝnis studied when the external forcing terms are unbounded in a phase space. The existence of a pullback global attractor for the equation is established inL2ℝn3andH1ℝn3, respectively. The pullback asymptotic compactness of solutions is proved by using uniform estimates on the tails of solutions on unbounded domains.

scholarly journals The global attractors and their Hausdorff and fractal dimensions estimation for the higher-order nonlinear Kirchhoff-type equation with nonlinear strongly damped terms

2016 ◽  
Vol 12 (10) ◽  
pp. 6658-6673
Author(s):  
Wei Wang ◽  
Ling Chen ◽  
Guoguang Lin
Keyword(s):  
Fractal Dimensions ◽  
Type Equation ◽  
Initial Boundary ◽  
Global Attractors ◽  
Time Behavior ◽  
Initial Boundary Value Problems ◽  
Long Time ◽  
Uniqueness Of The Solution ◽  
Hausdorff And Fractal Dimensions ◽  
Initial Boundary Value

In this paper ,we study the long time behavior of solution to the initial boundary value problems for higher -orderkirchhoff-type equation with nonlinear strongly dissipation:At first ,we prove the existence and uniqueness of the solution by priori estimate and Galerkin methodthen we establish the existence of global attractors ,at last,we consider that estimation of upper bounds of Hausdorff and fractal dimensions for the global attractors are obtain.

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