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1.
Ginzburg—Landau—Newell模型的动力学行为   总被引:2,自引:1,他引:1  
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。  相似文献   

2.
本文考虑通过Yukawa相互作用的耦合散Klein-Gordon-Schrodinger方程组的初边值问题,证明了整体吸引子的存在性。  相似文献   

3.
本文讨论Belousov-Zabotinskii化学反应Field-Noyes模型整体吸引子的存在性,维数估计以及性流形的存在性。  相似文献   

4.
平均熵   总被引:1,自引:0,他引:1  
设T为紧度量空间X上的连续自映射,m为X上的Borel概率测度,通过把测度(拓扑)摘局部化,引入了T关于m的平均测度(拓扑)熵的概念,它们分别为相应m-测度(拓扑)混沌吸引子熵的加权平均,从而T关于m的平均测度(拓扑)熵大于零当且仅当T有m-测度(拓扑)混沌吸引子.证明了线段I上关于Lebesgue测度平均拓扑熵大于C与等于零的连续自映射都在C0(I,I)中稠密.  相似文献   

5.
本文考虑了广义Fitz-Hugh-Nagumo方程组的初边值问题。去掉解属于某不变区域的限制,我们证明了初值属于L^2情形下整体吸引子的存在性,并给出其维数估计。  相似文献   

6.
吴珞 《应用数学学报》1998,21(3):463-470
本文将证明Navier-Stokes方程的解当t→+∞时趋于稳态解,并由此推出N-S方程存在集合满足泛吸引子或函数不变集条件的充要条件。  相似文献   

7.
Cahn-Hilliard方程的动力学稳定性   总被引:1,自引:0,他引:1  
李德生  李清仪 《数学学报》2000,43(1):127-134
考虑Cahn-Hilliard方程且a2p-1>0)的初边值问题,证明了系统在H1-H3中关于f系数的状动于H2中Hausdoorff半距离下稳定的全局吸引子的存在性.  相似文献   

8.
曹永罗 《数学学报》1999,42(6):965-968
本又考虑Lauwerier映射Fa,b(x,y)=(bx(1-2y)+y,ay(1-y)).我们证明对于参数α在一个正测度集合中,对应的映射有非平凡的拓扑可迁的吸引子,其中是某个双曲不动点的不稳定集的闭包.周期点是双曲的且在中稠密,而且中任两个周期点异宿相关(稳定与不稳定集的横截相交).同时也构造支撑在吸引子上的Sinal-Bowen-Ruelle测度,并研究其性质.  相似文献   

9.
1引言近年来.随着对无限维动力系统研究的深入,人们对非线性发展方程解的渐近性态了解得越来越多.例如对某些耗散的非线性发展方程,象Navier-Stokes方程、Kuramoto-Sivashin-sky方程等都存在整体的吸引子.系统的渐近性质和系统的复杂性完全由整体吸引子所确定(详细请参见[3]).与此同时,这类系统的有限维逼近也是人们非常关心的问题,在这方面已有许多工作,如J.K.Hale等人在[5]中基于有限元方法研究了某些非线性发展方程.得到了近似吸引子是上半连续的;C.M.Ellotta…  相似文献   

10.
Kuramoto-Sivashinsky方程的渐近吸引子   总被引:10,自引:0,他引:10  
本文给出了一周期边界条件下K-S方程的有限维渐进吸引子(Asymptotic Attractor)而非通常的近似吸引子(Approximate Attractor)。  相似文献   

11.
We consider submanifolds of non-isotropic planes of the Grassman manifold of the pseudo-Euclidean space. We prove a theorem about the unboundedness of the sectional curvature of the submanifolds of the two-dimensional non-isotropic planes of the four-dimensional pseudo-Euclidean space with the help of immersion in the six-dimensional pseudo-Euclidean space of index 3. We also introduce a concept of the indicatrix of normal curvature and study the properties of this indicatrix and the Grassman image of the non-isotropic surface of the pseudo-Euclidean space. We find a connection between the curvature of the Grassman image and the intrinsic geometry of the plane. We suggest the classification of the points of the Grassman image.  相似文献   

12.
Using the Monte Carlo method, we address the influence of the Wiener and Poisson random noises on the behavior of oscillatory solutions to systems of stochastic differential equations (SDEs). For the linear and Van der Pol oscillators, we study the accuracy of estimates of the functionals of numerical solutions to SDEs obtained by the generalized explicit Euler method. For a linear oscillator, we obtain the exact analytical expressions for the mathematical expectation and the variance of the SDE solution. These expressions allow us to investigate the dependence of the accuracy of estimates of the solution moments on the values of SDE parameters, the size of meshsize, and the ensemble of simulated trajectories of the solution. For the Van der Pol oscillator, we study the dependence of the frequency and the damping rate of the oscillations of the mathematical expectation of SDE solution on the values of parameters of the Poisson component. The results of the numerical experiments are presented.  相似文献   

13.
We prove some estimates on the spectrum of the Laplacian of the total space of a Riemannian submersion in terms of the spectrum of the Laplacian of the base and the geometry of the fibers. When the fibers of the submersions are compact and minimal, we prove that the spectrum of the Laplacian of the total space is discrete if and only if the spectrum of the Laplacian of the base is discrete. When the fibers are not minimal, we prove a discreteness criterion for the total space in terms of the relative growth of the mean curvature of the fibers and the mean curvature of the geodesic spheres in the base. We discuss in particular the case of warped products.  相似文献   

14.
15.
On the basis of the classical theory of thin anisotropic laminated plates the article analyzes the free vibrations of rectangular cantilever plates made of fibrous composites. The application of Kantorovich's method for the binomial representation of the shape of the elastic surface of a plate yielded for two unknown functions a system of two connected differential equations and the corresponding boundary conditions at the place of constraint and at the free edge. The exact solution for the frequencies and forms of the free vibrations was found with the use of Laplace transformation with respect to the space variable. The magnitudes of several first dimensionless frequencies of the bending and torsional vibrations of the plate were calculated for a wide range of change of two dimensionless complexes, with the dimensions of the plate and the anisotropy of the elastic properties of the material taken into account. The article shows that with torsional vibrations the warping constraint at the fixed end explains the apparent dependence of the shear modulus of the composite on the length of the specimen that had been discovered earlier on in experiments with a torsional pendulum. It examines the interaction and transformation of the second bending mode and of the first torsional mode of the vibrations. It analyzes the asymptotics of the dimensionless frequencies when the length of the plate is increased, and it shows that taking into account the bending-torsion interaction in strongly anisotropic materials type unidirectional carbon reinforced plastic can reduce substantially the frequencies of the bending vibrations but has no effect (within the framework of the binomial model) on the frequencies of the torsional vibrations.Institute of Engineering Science Russian Academy of Sciences, St. Petersburg, Russia. St. Petersburg State University, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 6, pp. 759–769, November–December, 1996.  相似文献   

16.
The dynamic contact problem of the motion of a flat punch on the boundary of an elastic half-plane is considered. During motion, the punch deforms the elastic half-plane, penetrating it in such a manner that its base remains parallel to the boundary of the half-plane at each instant of time. In movable coordinates connected to the moving punch, the contact problem reduces to solving a two-dimensional integral equation, whose two-dimensional kernel depends on the difference between the arguments for each of the variables. An approximate solution of the integral equation of the problem is constructed in the form of a Neumann series, whose zeroth term is represented in the form of the superposition of the solutions of two-dimensional integral equations on the coordinate semiaxis minus the solution of the integral equation on the entire axis. This approach provides a way to construct the solution of the two-dimensional integral equation of the problem in four velocity ranges of motion of the punch, which cover the entire spectrum of its velocities, as well as to perform a detailed analysis of the special features of the contact stresses and vertical displacements of the free surface on the boundary of the contract area. An approximate method for solving the integral equation, which is based on a special approximation of the integrand of the kernel of the integral equation in the complex plane, is proposed for obtaining effective solutions of the problem that do not contain singular quadratures.  相似文献   

17.
18.
We analyze the propagation of electromagnetic waves in the magnetic meridian planes of neutron stars with a strong magnetic field in the framework of the parameterized post-Maxwellian electrodynamics of the vacuum. The origin of these electromagnetic waves is the curvature emission of X-rays and gamma rays from high-energy electrons in the vicinity of the magnetic poles of neutron stars. We show that in the case of a slowly varying intensity of X-ray and gamma-ray emission, the delay of the slow normal mode of electromagnetic waves relative to the fast mode results in a shift of the time dependence of the intensity of the detected radiation with one polarization relative to that of the radiation with the orthogonal polarization. In the case of single X-ray or gamma-ray pulses, the delay effect results in the polarization of the detected pulse varying during the pulse length, the leading edge of all pulses being polarized normally to the magnetic equator plane of the neutron star. We note that the modern level of the experimental technique, in principle, allows observing the manifestations of the delay effect for signals of different polarizations.  相似文献   

19.
20.
The main terms of the asymptotic form of the solution of the contact problem of the compression without friction of an elastic body and a punch initially in point contact are constructed by the method of matched asymptotic expansions using an improved matching procedure. The condition of unilateral contact is formulated taking account of tangential displacements on the contact surface. An asymptotic solution of the problem for the boundary layer is constructed by the complex potential method. An asymptotic model is constructed, extending the Hertz theory to the case where the surfaces of the punch and elastic body in the vicinity of the contact area are approximated by paraboloids of revolution. The problem of determining the convergence of the contacting bodies from the magnitude of the compressive force is reduced to the problem of calculating the so-called coefficient of local compliance, which is an integral characteristic of the geometry of the elastic body and its fixing conditions.  相似文献   

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