共查询到17条相似文献,搜索用时 62 毫秒
1.
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。 相似文献
2.
3.
本在[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。 相似文献
4.
本文应用能量积分和解析半群的有关估计,研究广义二维Ginzburg-Landau方程 在Banach空间LP(Ω)的子空间X-α的指数吸引子. 相似文献
5.
6.
讨论二维全平面 Neiver- Stokes方程 tu -γ△ u αu u( .u) =f (x,t)∈Ω× R (1)div u =0 (2 )u(x,t)∈ H10 (Ω ) t>0 (3)u(x,0 ) =u0 (x)∈ H∩ H0 ,r (4 )其中Ω =R2 ,u =(u1,u2 )为速度场 ,f为外力 ,α >0 ,αu为与速度场平行的阻尼项 ,可理解为流体内部耗散的零阶近似 ,利用算子分解的方法 ,引入加权函数 ,我们证明问题 (1)~ (4 )在 H中存在指数吸引子 . 相似文献
7.
8.
本文在[1]的基础上,通过加权空间的紧性和算子的分解来构造H^2(R^1)的紧算子,证明了推广的B-BBM方程在H^2(R^1)中存在一个指数吸引子. 相似文献
9.
杜先云 《应用泛函分析学报》2003,5(1):41-48
研究了耗散Schroedinger-Boussinesq方程所生成的半群的性质,通过算子分解和构造渐近紧不变集,得到了该系统的指数吸引子。 相似文献
10.
带有阻尼项的广义对称正则长波方程的指数吸引子 总被引:2,自引:0,他引:2
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. 相似文献
11.
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. 相似文献
12.
In this paper, we consider a derivative Ginzburg-Landau-type equation with periodic initial-value condition in three-dimensional spaces. Sufficient conditions for existence and uniqueness of a global solution are obtained by uniform a priori estimates of the solution. Furthermore, the existence of a global attractor and an exponential attractor with finite dimensions are proved. 相似文献
13.
Abstract
In this paper, we establish the global fast dynamics for the derivative Ginzburg-Landau equation in two spatial dimensions.
We show the squeezing property and the existence of finite dimensional exponential attractors for this equation
* The author is supported by the Postdoctoral Foundation of China 相似文献
14.
The Ginzburg-Landau-type complex equations are simplified mathematical models for various pattern formation systems in mechanics,
physics, and chemistry. In this paper, the derivative complex Ginzburg-Landau (DCGL) equation in an unbounded domain Ω ⊂ ℝ2 is studied. We extend the Gagliardo-Nirenberg inequality to the weighted Sobolev spaces introduced by S. V. Zelik. Applied
this Gagliardo-Nirenberg inequality of the weighted Sobolev spaces and based on the technique for the semi-linear system of
parabolic equations which has been developed by M. A. Efendiev and S. V. Zelik, the global attractor
in the corresponding phase space is constructed, the upper bound of its Kolmogorov’s ɛ-entropy is obtained, and the spatial chaos of the attractor
for DCGL equation in ℝ2 is detailed studied.
相似文献
15.
Huang Haiyang 《应用数学学报(英文版)》2000,16(4):386-395
In this paper, we study the 2m-order nonlinear Ginzburg-Landau system inn spatial dimensions. We show the existence and uniqueness of the global generalized solution, and the existence of the global
attractor for this system, and establish the estimates of the upper bounds of Hausdorff and fractal dimensions for the global
attractor.
This project is supported by the National Natural Science Foundation of China (No. 19571010). 相似文献
16.
In this paper,the existence of global attractor for 3-D complex Ginzburg Landau equation is considered.By a decomposition of solution operator,it is shown that the global attractor A_i in H~i(Ω) is actually equal to a global attractor Aj in H~j(Ω)(i≠j,i,j = 1,2,…m). 相似文献
17.
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. 相似文献