弱阻尼非线性Schrodinger—Boussinesq方程整体吸引子的有限维性质

We Consider the following initlal-boundary problem of nonlinear Schrodingcr-Boussinesq eguations with weakly dampness in a hounded domain Ω of R^N :     

弱阻尼非线性Scdrodinger－Boussinesq方程整体吸引子的有限维性质

弱阻尼非线性Ｓｃｄｒｏｄｉｎｇｅｒ－Ｂｏｕｓｓｉｎｅｓｑ方程整体吸引子的有限维性质郭柏灵，陈风新ＦｉｎｉｔｅＤｉｍｅｎｓｉｏｎａｌＢｅｈａｖｉｏｒｏｆＧｌｏｂａｌＡｔｔｒａｃｔｏｒｓＦｏｒｗｅａｋｌｙＤａｍｐｅｄＮｏｎｌｉｎｅａｒＳｃｈｒｏｄｉｎｇｅ...     

离散FitzHugh-Nagumo方程的整体吸引子和维数

该文对ＦｉｔｚＨｕｇｈ Ｎａｇｕｍｏ方程初边值问题用有限差分格式离散空间变量,证明了离散模型整体吸引子的存在性,并给出了与犿无关的Ｈａｕｓｄｏｒｆｆ维数和Ｆｒａｃｔａｌ维数上界估计。     

非局部Kuramoto-Sivashinsky方程整体吸引子的维数估计

本文主要讨论NK-S方程整体吸引子的Hausdorff维数的上界估计.     

Rn上Plate方程全局吸引子的正则性和有限维性

研究了无界区域Rn上Plate方程全局吸引子的正则性和有限分形维性.该方程的全局吸引子在相空间H2(Rn)×L2(Rn)的存在性已在先期文章建立,现在进一步证明该全局吸引子具有更好的正则性,即它是H4(Rn)×H2(Rn)的有界集并具有有限分形维数．     

二维带形无界区域中Navier-Stokes方程整体吸引子及其维数估计

该文讨论二维无界带形区域中Navier-Stokes方程(I)u_t-△u+u_i(∂u)/∂x_i=-▽p+f(x,t)∈Ω×R₊(1)div u=0(2)u(X,t)∈H₀¹(Ω) for t>0(3) u(x,0)=u₀(x)∈H(4)其中Ω=(0,d)×R,d>0为一常数,u与p为未知量,其中u=(u₁,u₂)为速度场,p表示压力.我们证明了当u₀∈H,f∈V且f[log(e+x²)]^(1)/2∈L²(Ω)时,问题(I)在H中存在整体吸引子A,它是H₀²(Ω)的一个子集.对A的Hausdorff维数与Fractal维数我们也给出了估计.     

弱耗散抽象发展方程全局吸引子的存在性

采用定义泛函,忽略粘性阻尼项时,在特定空间中研究了弱耗散抽象发展方程,得到了该方程全局吸引子的存在性结论,丰富了该类方程全局吸引子存在性的证法.     

非线性Sobolev-Galpern方程的有限维整体吸引子

本文研究非线性Sobolev-Galpern方程解的渐近性态．首先证明了该方程在H^2(Ω)∩H0^1(Ω)中整体弱吸引子的存在性，然后利用一个能量方程证明了整体弱吸引子实际上是整体强吸引子，建立了整体吸引子的有限维性．     

The global attractors for the dissipative generalized Hasegawa-Mima equation

The long time behavior of solutions of the generalized Hasegawa-Mima equation with dissipation term is considered. The existence of global attractors of the periodic initial value problem is proved, and the estimate of the upper bound of the Hausdorff and fractal dimensions for the global attractors is obtained by means of uniform a priori estimates method.     

Analytical approach to estimating the dimension of attractors

A mathematically rigorous procedure to estimate the Hausdorff dimension of the attractor is given. The method is based on invoking the Kaplan-Yorke-type estimate, through extending the argument of Constantin, Foias, and Temam.This work is partially supported by Grant-in-Aid for Scientific Research (Nos. 04305031, 04554001, 04640209, and 05740082), Japan Ministry of Education, Science, and Culture.     

Global attractor and its dimension estimates for the generalized dissipative KdV equation onR

In this paper we prove the existence of global attractor for the generalized dissipative KdV equation onR, and give an upper bound for its hausdorff and fractal dimensions.     

Hausdorff dimension of cutset of complex valued rademacher series

Let{a.}.>1beasequenceofrealnumberssatisfyingEla.l~coandtiman=0.n=1n-cocoThenRademacherseriesZa.(l--Ze.(x))takeseverypreassignedrealvalueN(cardinaln=1numberofthecontinuum)timesforx6(0,1],whereE.(x)isthen-thdigitofthe(unique)non--terminating2--adicexpansionofx6(0,l].W.A.Beyer[1]showsthatif{a.}.>1Efi,{a.}411,thenforanyaCR,dimH{xE(0,1];Za.(1--26.(x))~a}~1;ifn=1co{a.}.21411,nlLmcoan~0,,Zla.--a.--if相似文献   

Global attractors for nonlinear wave equations with nonlinear dissipative terms

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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…     

Kernel sections for non-autonomous strongly damped wave equations

We prove the existence of compact kernel sections for the process generated by a non-autonomous strongly damped wave equation with homogeneous Dirichlet boundary condition. We show that the upper bound of the Hausdorff dimension of sections decreases as the damping grows for large strong damping.