Exponential Attractor for a Class of Nonclassical Diusion Equation

In this paper, we consider the asymptotic behavior of solutions for a class of nonclassical diffusion equation. We show the squeezing property and the existence of exponential attractor for this equation. We also make the estimates on its fractal dimension and exponential attraction.     

Exponential Attractor for Complex Ginzburg-Landau Equation in Three-dimensions

In this paper, we consider the complex Ginzburg-Landau equation (CGL) in three spatial dimensions u_t = ρu + (1 + iϒ )
Δu - (1 + iμ) |u|^{2σ} u, \qquad(1) u(0, x) = u_0(x), \qquad(2) where u is an unknown complex-value function defined in 3+1 dimensional space-time R^{3+1}, Δ is a Laplacian in R³, ρ > 0, ϒ, μ are real parameters. Ω ∈ R³ is a bounded domain. We show that the semigroup S(t) associated with the problem (1), (2) satisfies Lipschitz continuity and the squeezing property for the initial-value problem (1), (2) with the initial-value condition belonging to H²(Ω ), therefore we obtain the existence of exponential attractor.     

Davey-Stewartson方程在Banach空间中的指数吸引子

我们考虑了DS方程在Banach空间X^α_p中的指数吸引子,并且得到其分形维度估计.     

耗散MKdV方程的指数吸引子

讨论了无界区域R~1上的MKdV方程,运用带权空间构造一类紧算子和算子分解的方法,得到该方程在H~2（R~1）上指数吸引子的存在性.     

带有阻尼项的广义对称正则长波方程的指数吸引子

考虑了带有阻尼项的广义对称正则长波方程的整体快变动力学．证明了与该方程有关的非线性半群的挤压性质和指数吸引子的存在性．对指数吸引子的分形维数的上界也进行了估计．     

具有线性乘积白噪声的随机非自治吊桥方程的随机指数吸引子

本文考虑具有线性乘积白噪声的随机非自治吊桥方程长时间行为.首先,建立了所研究共圈系统的适定性;第二步,研究了该系统随机吸引子的存在性;第三步,当随机系数趋于0时,得到了随机吸引子的上半连续性;第四步,通过``迭代''法证明了随机吸引子在高正则空间中的正则性;最后,给出了该系统随机指数吸引子的存在性,同时得到了吸引子的有限分形维数.     

一维广义Ginzburg－Landau方程的指数吸引子

本文在[1]的基础上,得到了一维广义Ginzburg-Landau方程的指数吸引子的存在性。     

一类非线性发展方程的全局吸引子(英文)

本文研究了H01(Ω)×H01(Ω)上2≤r≤3时一类非自治发展方程的渐近行为,其中非线性项f满足临界指数增长。     

一类具有非线性kirchhoff-sine-Gordon广义方程的整体吸引子的存在性

主要目的是利用Galerkin逼近法和先验估计来证明一类具有非线性阻尼和外源项的耗散型sine-Gordon-kirchhoff方程的整体吸引子的存在性,首先通过先验估计证明系统存在唯一的整体解,再证明系统存在有界吸收集和算子半群光滑性质,最后得到系统存在整体吸引子.     

耦合非线性波方程的指数吸引子

在文[1]的基础上，得到了耦合非线性波方程的指数吸引子的存在性．     

Global Attractor for Weakly Damped Nonlinear Schrodinger-Boussinesq Equations in an Unbounded Domain

In this paper the authors consider the Cauchy problem of nonlinear Schrödinger-Boussinesq equations in R and prove the existence of the maximal attractor.     

Global Dynamics of a Nonlinear Beam Equation with Strong Structural Damping

In this paper, the global attractor, exponential attractor and flat inertial manifold are obtained for a nonlinear beam equation with strong structural damping.     

一类非线性差分方程的整体收敛性

利用[5]中的证明方法给出了一类非线性差分方程整体收敛性的一个充分条件,并将[1],[5]中的结果推广到更为一般的情形.     

Uniform Compact Attractors for a Nonlinear Non-Autonomous Equation of Viscoelasticity

In this paper we prove the regularity, exponential stability of global solutions and existence of uniform compact attractors of semiprocesses, generated by the global solutions, of a two-parameter family of operators for a nonlinear onedimensional non-autonomous equation of viscoelasticity. We employ the properties of the analytic semigroup to show the compactness for the semiprocess generated by the global solutions.     

Global Existence and Exponential Decay for a Nonlinear Viscoelastic Equation with Nonlinear Damping

In this paper we investigate a nonlinear viscoelastic equation with nonlinear damping. Global existence of weak solutions and uniform decay of the energy have been established. The Faedo-Galerkin method and the perturbed energy method are employed to obtain the results.     

Asymptotic behavior for the singularly perturbed damped Boussinesq equation

This work is focused on the long‐time behavior of solutions to the singularly perturbed damped Boussinesq equation in a 3D case where ε > 0 is small enough. Without any growth restrictions on the nonlinearity f(u), we establish in an appropriate bounded phase space a finite dimensional global attractor as well as an exponential attractor of optimal regularity. The key step is the estimate of the difference between the solutions of the damped Boussinesq equation and the corresponding pseudo‐parabolic equation.Copyright © 2014 John Wiley & Sons, Ltd.     

非线性Schroedinger方程的整体吸引子

本文讨论了一类带调和势｜x｜^2的非线性Schroedinger方程解的长时间行为，证明了整体吸引子的存在性．     

一类非经典反应扩散方程全局吸引子的正则性

考虑了一类非经典反应扩散方程全局吸引子的正则性。利用渐近先验估计证明了系统在H01(Ω)中的全局吸引子A1在D(A)中有界,并进一步获得A1即为系统在D(A)中的全局吸引子A2。