复Ginzburg Landau方程的自相似解及其极限行为

该文证明了复Ginzburg Landau方程在非标准的函数空间X_{s,p}中整体解的存在唯一性；考察了其解在X_{0,α+2}中的极限行为，得到当参数ε→0++或a→0, ε→0++时，Ginzburg Landau方程的解关于时间一致收敛到相应极限方程的解     

三维复Ginzburg-Landau方程的整体解的存在惟一性

在三维空间中研究带2σ次非线性项的复值Ginzburg—Landau方程(CGL) ut=ρu (1 iγ)△u-(1 iμ)|u|^2σu,通过先验估计的方法,在适当的σ的假设下,获得该方程周期边值问题整体解的存在性和惟一性．     

人口问题中的三维Ginzburg-Landau模型方程的Cauchy问题

本文证明人口问题中的三维Ginzburg－Landau模型方程的周期边值问题和Cauchy问题的广义解和古典解的整体存在性、唯一性以及解的渐进性质．     

广义Ginzburg-Landau方程和Rangwala Rao方程的显式精确解

该文通过适当代换并结合假设待定法，求出了具高阶非线性项的Liénard方程a″(ξ)+la(ξ)+ma\+\{2p+1\}(ξ)+na\+\{4p+1\}(ξ)=0的三类精确解. 据此求出了广义Ginzburg Landau方程、Rangwala Rao方程及若干 导数schr〖AKo¨D〗dinger型方程的孤波解和三角函数型周期波解.     

二维广义Ginzburg-Landau方程的指数吸引子

在文[1]的基础上，得到了二维广义的Ginzburg－Landau方程的指数吸引子的存在性．     

Ginzburg-Landau旋涡与调和映射的自相似解

得到了带pinning效应的Ginzburg Landau方程组的H1 紧性 ,证明了其二维情况的旋涡被pinning函数的最小点所吸引 ,构造了调和映射发展方程的自相似解     

关于增生算子方程解的带误差的Ishikawa迭代程序

该文在Banach空间中证明了，带误差的Ishikawa迭代序列强收敛到Lipschitz连续的增生算子方程的唯一解．而且，也给Ishikawa迭代序列提供了一般的收敛率估计．利用该结果还推得，带误差的Ishikawa迭代序列也强收敛到Lipschitz连续的强增生算子方程的唯一解．     

含有杂质的Ginzburg-Landau泛函的径向极小元

研究了含有杂质的超导体的Ginzburg—Landau模型，给出了Ginzburg—Landau泛函的径向极小元的零点分布，并证明了径向极小元的惟一性。     

一类非齐次A 调和方程组很弱解的性质

该文应用Hodge分解定理，得到了非齐次A 调和方程组 -D\-i(A\+\{ij\}(x,Du))+D\-if\+i\-j(x)=0, j=1, \:, m的很弱解是弱解，进一步，利用Morrey空间法与Campanato空间法以及齐次化方法，作者得出了该方程的很弱解是局部H[AKo¨D]lder连续的，并且得出了H[AKo¨D]lder连续指数μ与λ之间的多值函数关系式。     

广义系统的Hamilton矩阵与H\-2代数Riccati方程的稳定化解

研究线性连续广义系统的Hamilton矩阵及H\-2代数Riccati方程.　提出一个标准的广义H\-2代数Riccati方程及对应的Hamilton矩阵，给出该Hamilton矩阵的几个重要性质. 在此基础上，得到该广义H\-2代数Riccati方程的稳定化解存在的一个充分条件并给出求解方法.此条件具有一般性, 主要定理是正常系统相应结果的推广.     

On the Global Attractor of Generalized Ginzburg-Landau Equation in One Spatial Dimension

The target of this paper is the long time behaviour of solutions for a generalized Ginzburg-Landau equation on IR. The authors establish the existence of a global attractor of finite Hausdorff and fractal dimension in a weighted Hilbert space for the equation.     

ATTRACTORS FOR THE GINZBURG-LANDAU-BBM EQUATIONS IN AN UNBOUNDED DOMAIN

1IntroductionInthispaper,weintendtostudytheexistenceoftheglobalattractorforthefollowinginitialvalueproblemofGinzburgLandauequationcoupledwithBBMequationinanunboundeddomainR=(-oo,oo)wheree(x,f)isacomplexfunction,n(x,t)isarealscalarfunction,pty,6,T,cr1,a2,P1,P2arerealcoustants,andg1(x),g2(x)aregivenrealfunctions.ThisproblemdescribesthenonlinearinteractionsbetweentheLangnluirwaveandtheionacousticwaveinplasmaphysics,E(z,t)denoteselectricfield,n(x,t)betheperturbationofdensity(see[2,12,6l).In[7]…     

Attractors for generalized Ginzburg-Landau-BBM equations in an unbounded domain

By the interpolation inequality and a priori estimates in the weighted space, the existence of global solutions for generalized Ginzburg-Landau equation coupled with BBM equation in an unbounded domain is considered, and the existence of the maximal attractor is obtained. This research is supported by the National Natural Science Foundation of China (No.19861004).     

Weak solutions to the two-dimensional derivative Ginzburg-Landau equation

1.IntroductionInthepreselltpaper)westudythefollowinggeneralizedcomplexGinzburg-Landauequationintwospatialdimensions:anm=pp (1 in)au~(1 lp)Ill'"~ ox,.v(lul'u) p(x,.ac)lul',(1.1)whereallparametersarereal.Thisequation3mostlyconsideredwithor=P=0anda=1,hasalongandbroadhistoryinphysicsasagenericamplitudeequationneartheonsetofinstabilitiesinfluidmechanicalsystems,aswellasinthetheoryofphasetransitionsandsuperconductivity.Inthstspecialcase,theekistenceofsolutionsandtheirlongtimebehaviourhavebeeninves…     

Exponential Attractors for the Generalized Ginzburg-Landau Equation

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     

On the connectedness and asymptotic behaviour of solutions of reaction-diffusion systems

In this paper we consider reaction-diffusion systems in which the conditions imposed on the nonlinearity provide global existence of solutions of the Cauchy problem, but not uniqueness. We prove first that for the set of all weak solutions the Kneser property holds, that is, that the set of values attained by the solutions at every moment of time is compact and connected. Further, we prove the existence and connectedness of a global attractor in both the autonomous and nonautonomous cases. The obtained results are applied to several models of physical (or chemical) interest: a model of fractional-order chemical autocatalysis with decay, the Fitz-Hugh-Nagumo equation and the Ginzburg-Landau equation.     

Convergence towards attractors for a degenerate Ginzburg-Landau equation

We study a real Ginzburg-Landau equation, in a bounded domain of \mathbbR^N ,\mathbb{R}^N , with a variable, generally non-smooth diffusion coefficient having a finite number of zeroes. By using the compactness of the embeddings of the weighted Sobolev spaces involved in the functional formulation of the problem, and the associated energy equation, we show the existence of a global attractor. The extension of the main result in the case of an unbounded domain is also discussed, where in addition, the diffusion coefficient has to be unbounded. Some remarks for the case of a complex Ginzburg-Landau equation are given.     

Convergence towards attractors for a degenerate Ginzburg-Landau equation

We study a real Ginzburg-Landau equation, in a bounded domain of with a variable, generally non-smooth diffusion coefficient having a finite number of zeroes. By using the compactness of the embeddings of the weighted Sobolev spaces involved in the functional formulation of the problem, and the associated energy equation, we show the existence of a global attractor. The extension of the main result in the case of an unbounded domain is also discussed, where in addition, the diffusion coefficient has to be unbounded. Some remarks for the case of a complex Ginzburg-Landau equation are given.Received: May 6, 2002; revised: October 3, 2002     

Some Properties of Solutions to the Novikov Equation with Weak Dissipation Terms

In this paper, we investigate the Novikov equation with weak dissipation terms. First, we give the local well-posedness and the blow-up scenario. Then, we discuss the global existence of the solutions under certain conditions. After that, on condition that the compactly supported initial data keeps its sign, we prove the infinite propagation speed of our solutions, and establish the large time behavior. Finally, we also elaborate the persistence property of our solutions in weighted Sobolev space.     

Hopf Bifurcation in Spatially Extended Reaction—Diffusion Systems

Summary. We consider weakly unstable reaction—diffusion systems defined on domains with one or more unbounded space-directions. In the systems which we have in mind, at criticality, the most unstable eigenvalue belongs to the wave vector zero and possesses a nonvanishing imaginary part. This instability leads to an almost spatially homogeneous Hopf-bifurcation in time. A standard example is the Brusselator in certain parameter ranges. Using multiple scaling analysis we derive a Ginzburg-Landau equation and show that all small solutions develop in such a way that they can be approximated after a certain time by the solutions of the Ginzburg-Landau equation. The proof differs essentially from the case when the bifurcating pattern is oscillatory in space. Our proof is based on normal form methods. As a consequence of the results, the global existence in time of all small bifurcating solutions and the upper-semicontinuity of the original system attractor towards the associated Ginzburg-Landau attractor follows. Original received February 21, 1996; revision accepted April 16, 1997