有阻尼Sine－Gordon方程的全局吸引子的维数

本文通过引入新范数,得到有阻尼Ｓｉｎｅ－Ｇｏｒｄｏｎ方程的Ｄｉｒｉｃｈｌｅｔ问题的全局吸引子的维数的一个估计．结果表明：当“阻尼”与“扩散”同时增大或正弦项系数减小时,吸引子的维数减小．特别地,得到了零维吸引子存在的参数条件．     

具阻尼的非线性波动方程整体吸引子的Hausdorff维数、分形维数估计

本文得到了一类具有线性阻尼且非线性项满足临界增长条件的非线性波动方程整体吸引子的Hausdorff维数、分形维数估计．     

Sine—Gordon方程的全局吸引子的维数估计

本文得到了阻尼Ｓｉｎｅ－Ｇｏｒｄｏｎ方程的狄氏问题的全局吸引子的Ｈａｕｓｄｏｒｆｆ维数以偶数上界的参数条件，特别地，当阻尼与Ｌａｐｌａｅ算子的第一个特征值适当大时，全局吸引子是零维的，零维吸引子恰是系统的唯一平衡解并且指数吸引相空间的有界集。     

具阻尼的非线性波动方程整有引子的Hausdorff维数,分形维数估计

本文得到了一类具有线性阻尼且非线性项满足临界增长条件的非线性波动方程整体吸引子的Ｈａｕｓｄｏｒｆｆ维数，分形维数估计。     

弱阻尼广义KdV方程的整体吸引子

证明了具有弱阻尼项的广义KdV方程约周期初边值问题解的存在唯—性及整体吸引子存在性,最后获得了吸引子的Hausdorff维数和分形维数的上界估计．     

Ginzburg－Landau－Newell模型的动力学行为

木文对Ｇｉｎｚｂｕｒｇ－Ｌａｎｄａｕ－Ｎｅｗｅｄ模型的动力学行为进行了讨论，得到了该模型的整体吸引子的存在性，同时得到了此吸引子维数的下界估计和该吸引子的Ｈａｕｓｄｏｒｆｆ维数和Ｗａｃｔａｌ（分形）维数的上界估计．     

离散的Burgers-Ginzburg-Landau方程组的吸引子

文章通过对空间变量的有限差分方法离散了具有周期边值的Ｂｕｒｇｅｒｓ Ｇｉｎｚｂｕｒｇ Ｌａｎｄａｕ方程组．研究了这个离散方程组初值问题解的适定性．证明了当差分网格足够大时离散方程组存在吸引子，并得到了吸引子的Ｈａｕｓｄｏｒｆｆ维数和分形维数的上界估计．这个上界不会随着网格的加细而无限增大，因此数值分析离散的有限维系统的吸引子可以近似探讨原无限维系统的吸引子．     

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．     

Ginzburg—Landau—Newell模型的动力学行为

本文对Ｇｉｎｚｂｕｒｇ－Ｌａｎｄａｕ－Ｎｅｗｅｌｌ模型的动力学行为进行了讨论，得到了该模型的整体吸引子的存在性，同时得到了此吸引子维数的下界估计和该吸引子的Ｈａｕｓｄｏｒｆｆ维数和Ｆｒａｃｔａｌ维数的上界估计。     

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     

Finite and Infinite-Dimensional Attractors of Multivalued Reaction-Diffusion Equations

We study the fractal dimension of the global attractor generated by a multivalued reaction-diffusion equation for which there is no uniqueness of solutions. First we give an example of a global attractor having infinite fractal dimension. Then under certain conditions we obtain an estimate of the fractal dimension. This revised version was published online in June 2006 with corrections to the Cover Date.     

阻尼Navier-Stokes系统的渐近吸引子

本文通过构造一个有限维解序列,研究了二维阻尼驱动Navier-Stokes方程的渐近吸引子,并证明了该解序列在长时间内无限逼近全局吸引子,最后给出了渐近吸引子的维数估计.     

Dimension of the global attractor for the discretized damped sine-Gordon equation

This paper presents a more precise estimate on the dimension of the global attractor for spatially discretized damped sine-Gordon equation with periodic boundary condition. The gained Hausdorff dimension is consistent with the continuous case and conforms to physics.     

Attractor and dimension for strongly damped nonlinear wave equation

1. IntroductionConsider the strongly damped nonlinear wave equationwith the Dirichlet boundary conditionand the initial value conditionswhere u = u(x, t) is a real--valued function on fi x [0, co), fi is an open bounded set of R"with smooth boundary off, or > 0, g e L'(fl), D(--Q) ~ Ha(~~) n H'(fl).We assume for the function f(u) as follows'f(u) E CI (R, R) satisfiesfor any ig al, uZ E R, where k, hi > 0, i ~ 0, 1, 2, 61 > 0 and 0 5 6o < 1'The type of equation (1) can be regarded as the…     

Finite dimensionality of global attractors for a non-classical reaction-diffusion equation with memory

In this paper, we consider a periodic boundary value problem for a non-classical reaction-diffusion equation with memory. In other paper, we use the ω-limit compactness of the solution semigroup {S(t)}_t≥0 to get the existence of a global attractor. The main goal here is to give an estimate of the fractal dimension of the global attractor. By the fractal dimension theorem given by A.O. Celebi et al., we obtain that the fractal dimension of the global attractor for the problem is finite; this makes the results for the non-classical reaction-diffusion equations more substantial and perfect.     

Dimension of the global attractor for damped nonlinear wave equations

An estimate on the Hausdorff dimension of the global attractor for damped nonlinear wave equations, in two cases of nonlinear damping and linear damping, with Dirichlet boundary condition is obtained. The gained Hausdorff dimension is bounded and is independent of the concrete form of nonlinear damping term. In the case of linear damping, the gained Hausdorff dimension remains small for large damping, which conforms to the physical intuition.

     

A note on the dimension of the global attractor for an abstract semilinear hyperbolic problem

We study a semilinear hyperbolic problem, written as a second-order evolution equation in an infinite-dimensional Hilbert space. Assuming existence of the global attractor, we estimate its fractal dimension explicitly in terms of the data. Despite its elementary character, our technique gives reasonable results. Notably, we require no additional regularity, although nonlinear damping is allowed.     

An estimate for the Hausdorff dimension of attractor for two-dimensional equations of Oldroyd fluids

The minimal global B-attractor for a system of equations describing two-dimensional flows of Oldroyd fluids is considered. An asymptotic estimate for the Hausdorff dimension of the attractor is obtained for small values of the viscosity. Bibliography: 11 titles. Translated fromZapiski Nauchnykh Seminarov POMI Vol. 226, 1996, pp. 109–119.