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1.
该文讨论二维无界带形区域中Navier-Stokes方程其中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+|x|2)]1/2∈L2(Ω)时,问题(I)在H中存在整体吸引子A,它是的一个子集.对A的Hausdorff维数与Fractal维数我们也给出了估计.  相似文献   

2.
该文讨论二维无界带形区域中Navier-Stokes方程(Ⅰ){ut-△u+uiэuэxi=-△p+f(x,t)∈Ω×R+(1)divu=0(2)u(X,t)∈(H^10(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+│x│^2)」^12∈L  相似文献   

3.
§1. IntroductionAtfirst,weintroduceournotations.Wedenotetheclassofallsquare-integrable2π-periodicfunctionsbyL22π,thatis,L22π={f(x)|f(x)=f(x+2π),x∈R,∫2π0|f(x)|2dx<∞}.  Foranyf(x),g(x)∈L22π,theinnerproduct〈f,g〉isdefinedas〈f,g〉:=12π∫2π0f(x)g(x)dx.(1.1) …  相似文献   

4.
§1 IntroductionInthispaperwecontinuetoconsidertheexistenceofpositiveradialsolutionsforthequasilinearellipticequation-div(|Du|p-2Du)=f(u) inΩ,(1)u(x)=0 onΩ,wherex∈Rn,n≥2,Ω={x:a<|x|<b,a,b>0},andp>1,f∈C1((0,∞))∩C0([0,∞))satisfyingthefollowinghypotheses…  相似文献   

5.
在文中,对于C^m中有界强拟凸域Ω,得到了Bergman空间A^2(Ω)上的Hankel算子Hf(f∈L^2(Ω,dv)的本性范数∥Hf∥ess(在L^2(Ω,dv上)的等价刻划。  相似文献   

6.
一种级的维数   总被引:1,自引:0,他引:1  
令f(x)=∑n≥1,b^sn-2g(bnx),其中S∈(1,2),对n∈z,g(4n+x(  相似文献   

7.
岳优兰  王月山 《数学季刊》1999,14(2):108-110
§1. IntroductionAlocallyintegrablefunctionf(x)belongstoLipα(Rn),ifthereisaconstantC,suchthatforeveryx,y∈Rn|f(x)-f(y)|≤C|x-y|α  ThesmallestconstantCsatisfiesaboveiscalledLipschitznormoffandisdenotedbyyfy∧α.By[1],f∈Lipα(Rn)equivalenttof∈εα,2,whereεα,2=…  相似文献   

8.
胡克 《数学杂志》1993,13(4):413-418
设f(z)=z+Σanz^n为单位园|z|<1内解析且平均单叶,记其族为M又设{f(z)/z}^λ=1+Σ^∞n=1Dn(λ),λ>0,本文说明了:定理一 若f∈M,λ>0,则:Σ^∞k=1{||Dk(λ)|-|Dk-1(λ)||/dk(λ)}^2≤An,n=2,3,…其中A为绝对常数。dk(h)=h(h+1)…(h+k-1)/k!当λ=1/2,f∈s时为I.V.Milm所证明。定理二 若f∈M并  相似文献   

9.
非线性波动与社会传播混合型方程的整体紧吸引子   总被引:3,自引:0,他引:3  
本文研究非一波动与神经传播混合型方程utt=uxxt+σ(ux)x-h(u)ut-f(u)+g(x)初边值问题的整体吸引子,在σ∈C^2,σ(s)〉σ0〉0及h(s)∈C^1,-Co〈h(s)(0〈Co〈λ1/2)且∫o^uh(s)sds〈Cu^2条件下我们得到了与该方程相应的动力系统整体紧吸引子的存在性,并证明了它具有有限的Hausdorffx维数和fractal维数。  相似文献   

10.
本文研究二维全空间上线性阻尼Navier-Stokes方程的大时间性态央餐力项f(x)∈(L^2(R^2)^2而不需要对f(x)作任何加权限制的条件下,证明了线性阻尼Navier-Stokes方程的全局吸引子的存在性,并给出了其Hausdorff及Fractal维数估计。  相似文献   

11.
We present an algorithm for finding the global maximum of a multimodal, multivariate function for which derivatives are available. The algorithm assumes a bound on the second derivatives of the function and uses this to construct an upper envelope. Successive function evaluations lower this envelope until the value of the global maximum is known to the required degree of accuracy. The algorithm has been implemented in RATFOR and execution times for standard test functions are presented at the end of the paper.Partially supported by NSF DMS-8718362.  相似文献   

12.
In this paper, a chemotaxi model with reproduction term in a bounded domain Ω ⊂ Rn is discussed. The existence of a global-in-time solution and a global attractor for this model are obtained.  相似文献   

13.
In this paper, a chemotaxis model with reproduction term in a bounded domain R n is discussed. The existence of a global-in-time solution and a global attractor for this model are obtained.  相似文献   

14.
15.
A general iterative method is proposed for finding the maximal rootx max of a one-variable equation in a given interval. The method generates a monotone-decreasing sequence of points converging tox max or demonstrates the nonexistence of a real root. It is globally convergent. A concrete realization of the general algorithm is also given and is shown to be locally quadratically convergent. Computational experience obtained for eight test problems indicates that the new method is comparable to known methods claiming global convergence.  相似文献   

16.
17.
填充函数法是求解全局优化问题的一种有效的确定性算法,方法的关键在于填充函数的构造.对于一般无约束优化问题提出了一个新的无参数填充函数,通过定义证明了此填充函数能保持填充性质.利用其理论性质设计了相应的算法并对几个经典的算例进行了数值实验,实验结果表明算法有效可行.  相似文献   

18.
填充函数法是求解全局优化问题的一个重要的确定性算法,这种方法的关键是构造具有良好性质的填充函数.构造了一个新的求解无约束全局优化问题的填充函数.函数连续可微且只包含一个参数.通过分析该函数的相关性质,设计了相应的算法.数值实验表明该算法简单有效.  相似文献   

19.
时滞Hopfield神经网络模型的全局吸引性和全局指数稳定性   总被引:6,自引:0,他引:6  
对具有时滞的Hopfield神经网络模型,在非线性神经元激励函数是Lipschitz连续(而非已有的大部分文献中假设是Sigmoid函数)的条件下,通过构造适当的泛函,给出了这类模型全避吸引和平衡点全局指数稳定的易于验证的充分条件。  相似文献   

20.
In this paper, we investigate the Cauchy problem for a class of the system of semilinear hyperbolic equations with damping. With the use of the LpLq type estimation for the corresponding linear problem and the method of comparison of functional, the existence and nonexistence criteria of global solutions are found. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

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