The Upper Semicontinuity of Random Attractors for Non-Autonomous Stochastic Plate Equations with Multiplicative Noise and Nonlinear Damping

Based on the existence of pullback attractors for the non-autonomous stochastic plate equations with multiplicative noise and nonlinear damping defined in the entire space $\mathbb{R}^n$ by Xiaobin Yao in \cite{Yao4}, in the paper, we further investigate the upper semicontinuity of pullback attractors for the problem.     

Global attractors for porous-elasticity system from second spectrum viewpoint

This paper is concerned with the global attractors for a new partially damped porous-elasticity system by taking a truncated version which is free of blow-up on second wave speed. We establish the global well-posedness of the system via Faedo–Galerkin method. By considering only one damping term acting on the volume fraction in the system we prove the existence of absorbing set for the solution semigroup regardless any relationship between coefficients of the system. Finally, by using Lyapunov and recent quasi-stability methods we prove the existence of smooth global attractors with finite fractal dimension.     

Uniform attractors for a nonautonomous extensible plate equation with a strong damping

In this paper, we study the long‐time dynamics of solutions to a nonlinear nonautonomous extensible plate equation with a strong damping. Under some suitable assumptions on the initial data, the nonlinear term and external force, we establish the existence of global solutions that generate a family of processes for the problem and obtain uniform attractors corresponding to strong and weak symbol spaces in a bounded domain . Copyright © 2016 John Wiley & Sons, Ltd.     

Finite dimensionality of the global attractors for von Karman equations with nonlinear interior dissipation

In this paper we study the global attractors for von Karman equations with nonlinear interior dissipation. We prove regularity and then establish finite dimensionality of the global attractors without assuming large values for the damping parameter.     

Long Time Behavior of Nonlinear Strain Waves in Elastic Waveguides

The initial-boundary value problem of the propagation of nonlinear longitudinal elastic waves in an initially strained rod is considered. The rod is assumed to interact with the surrouding elastic and viscous external medium. The long time behavior of solutions is derived ancl global attractors in E_1 space is obtained.     

Pullback attractors for non-autonomous porous elastic system with nonlinear damping and sources terms

In this paper, we study the asymptotic behavior of a non-autonomous porous elastic systems with nonlinear damping and sources terms. By employing nonlinear semigroups and the theory of monotone operators, we establish existence and uniqueness of weak and strong solutions. We also prove the existence of minimal pullback attractors with respect to a universe of tempered sets defined by the sources terms. Finally, we prove the upper-semicontinuity of pullback attractors with respect to non-autonomous perturbations.     

GLOBAL ATTRACTOR OF NONLINEAR STRAIN WAVES IN ELASTIC WAVEGUIDES

1 IntroductionIn some problelm of nonlineax wave propagation in waveguides, the interaction of waveguides and the external medium and, therefore, the possibility of energy exchange through laternal surfaCe of waveguide cannot be neglected,when the energy exchange between the rodand the medium is considered, for one easel there is a dissipation of a deformation wave in theviscous external medium, the general cubic double dispersion equation (CDDE) can be denyedfrom Hamilton principle[']where …     

Global and exponential attractors for mixtures of solids with Fourier’s law

This paper presents a study of the long-time dynamics of the dynamical system generated by a nonlinear system modeling mixture of solids with nonlinear damping and Fourier’s law. By using the recent quasi-stability theory, we prove the existence of a smooth finite dimensional global attractor, which is characterized as an unstable manifold of the set of stationary solutions. The quasi-stability of the system is achieved through an estimated stabilizability. Moreover, the existence of a generalized exponential attractor is shown.     

Global attractor for hyperbolic equation with nonlinear damping and linear memory

In this paper, we study the existence of global attractors for the hyperbolic equation with nonlinear damping and linear memory.     

非线性梁方程强全局吸引子的存在性

非线性梁方程描述了桥面在竖直平面内的振动.作者利用文献[3]中给出的一种新的验证紧性的方法讨论了这类方程强解的全局吸引子.     

非线性Kirchhoff型波动方程全局吸引子的存在性

非线性Kirchhoff型波动方程描述了竖直方向上的波动.利用近似FaedoGalerkin的方法通过先验估计和一种新的验证紧性的方法(条件C)讨论了这类波动方程强解的全局吸引子.     

Quasi-stability and upper semicontinuity for coupled parabolic equations with memory

This current study deals with the long-time dynamics of a nonlinear system of coupled parabolic equations with memory. The system describes the thermodiffusion phenomenon where the fluxes of mass diffusion and heat depend on the past history of the chemical potential and the temperature gradients, respectively, according to Gurtin-Pipkin's law. Inspired by the works of Chueshov and Lasiecka on the property of quasi-stability of dynamic systems, we prove this property for the problem considered in this study. This property allows us to analyze certain properties of global and exponential attractors in a more efficient and practical way. This approach is applied for the first time for coupled parabolic equations. We analyze the continuity of global attractors with respect to a pair of parameters in a residual dense set and their upper semicontinuity in a complete metric space. Finally, we analyze the upper semicontinuity of global attractors with respect to small perturbations of the damping terms.     

Global and exponential attractors for 3‐D wave equations with displacement dependent damping

A weakly damped wave equation in the three‐dimensional (3‐D) space with a damping coefficient depending on the displacement is studied. This equation is shown to generate a dissipative semigroup in the energy phase space, which possesses finite‐dimensional global and exponential attractors in a slightly weaker topology. Copyright © 2006 John Wiley & Sons, Ltd.     

一类二维非线性Schrodinger方程的吸引子及其维数

本文研究了一类二维非线性Ｓｃｈｒｏｄｉｎｇｅｒ方程解的有限维行为，我们得到了此方程存在吸引子，并得到了此吸引子维数的上界估计     

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

In this paper, we study the existence of global attractors for the extensible beam equation with localized nonlinear damping and linear memory. Copyright © 2011 John Wiley & Sons, Ltd.     

The Global Attractors for the Periodic Initial Value Problem of Generalized Kuramoto-Sivashinsky Type Equations in Multi-dimensions

The existence of global attractors for the periodic initial value problem of generalized Kuramoto-Sivashinsky type equations in multi-dimensions is proved. We also get the estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractors by means of a uniform priori estimates for time.     

A global attractor for the plate equation with displacement-dependent damping

We study the long-time behaviour of solutions of the plate equation with nonlinear damping coefficient. We prove under suitable conditions that this equation possesses a global attractor.     

Pullback attractors of 2D Navier–Stokes equations with weak damping,distributed delay,and continuous delay

In this present paper, the existence of pullback attractors for the 2D Navier–Stokes equation with weak damping, distributed delay, and continuous delay has been considered, by virtue of classical Galerkin's method, we derived the existence and uniqueness of global weak and strong solutions. Using the Aubin–Lions lemma and some energy estimate in the Banach space with delay, we obtained the uniform bounded and existence of uniform pullback absorbing ball for the solution semi‐processes; we concluded the pullback attractors via verifying the pullback asymptotical compactness by the generalized Arzelà–Ascoli theorem. Copyright © 2016 John Wiley & Sons, Ltd.     

Well-posedness and dynamics for the fractional Ginzburg-Landau equation

This article studies the global well-posedness and long-time dynamics for the nonlinear complex Ginzburg–Landau equation involving fractional Laplacian. The global existence and some uniqueness criterion of weak solutions are given with compactness method. To study the strong solutions with the semigroup method, we generalize some pointwise estimates for the fractional Laplacian to the complex background and study carefully the linear evolution of the equation. Finally, the existence of global attractors is studied.     

一类非线性非自治可伸缩板方程的一致吸引子

讨论了一类带有初值条件和固定边界条件的非线性非自治可伸缩板方程u_(tt)+△~2u+αu-△u_(tt)-M(||▽u||~2)△u-γ△u_t+f(u)=σ(x,t)证明了该系统的整体适定性.进一步研究了该系统的长时间动力学,利用建立整体弱解所生成的半过程一致渐近紧性,得到了有界区域Ω■R~n(n≥1)或无界开集中一致吸引子的存在性.