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1.
离散FitzHugh-Nagumo方程的整体吸引子和维数   总被引:2,自引:0,他引:2       下载免费PDF全文
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。  相似文献   

2.
带五次项的NLS方程及其谱逼近的整体吸引子的维数估计   总被引:1,自引:0,他引:1  
通过给出一般发展方程和其近似方程解的整体吸引子的Hausdorff维数上界间的关系,继[1,2]的讨论,本文进一步得到了带五次项的NLS方程和半离散Fourier谱近似解的整体吸引子的Hausdorff维数的上界估计。  相似文献   

3.
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   

4.
推广的B-BBM方程的整体吸引子和指数吸引子   总被引:7,自引:1,他引:6  
朱朝生  蒲志林 《应用数学》2003,16(2):134-138
本文对耗散的推广的B-BBM方程的长时间动力学行为进行了研究,证明了该方程整体吸引子和指数吸引子的存在性。  相似文献   

5.
黄建华  路钢 《数学杂志》2002,22(3):354-358
本文用有限差分格式对FitzHugh-Nagumo方程的时间变量和空间变量同时离散,给出了离散模型整体吸引子存在的条件。  相似文献   

6.
黄建华  路钢 《应用数学》2003,16(4):107-116
本文研究了广义耦合FitzHugh—Nagumo方程及广义离散耦合FitzHugh-Nagumo方程,分别证明了连续模型及离散模型整体吸引子的存在性,并给出了其Huasdorff维数估计,其中离散模型的Hausdorff维数上界与n无关.  相似文献   

7.
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   

8.
在本文中,我们通过引入一类Frechet空间,得到了三维有界光滑区域上的地磁流方程的弱解的整体吸引子的存在性。  相似文献   

9.
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   

10.
在本文中,环状区域中的轴对称Kuramoto-Sivashinsky方程的有限维整体吸引子被得到了.  相似文献   

11.
We describe a backward error analysis for stochastic differential equations with respect to weak convergence. Modified equations are provided for forward and backward Euler approximations to Itô SDEs with additive noise, and extensions to other types of equation and approximation are discussed.  相似文献   

12.
Based on the fact that the Painlevé equations can be written as Hamiltonian systems with affine Weyl group symmetries, a canonical quantization of the Painlevé equations preserving such symmetries has been studied recently. On the other hand, since the Painlevé equations can also be described as isomonodromic deformations of certain second-order linear differential equations, a quantization of such Lax formalism is also a natural problem. In this paper, we introduce a canonical quantization of Lax equations for the Painlevé equations and study their symmetries. We also show that our quantum Lax equations are derived from Virasoro conformal field theory.  相似文献   

13.
We propose several approaches for solving two discrete-velocity Boltzmann equations using the rescaling ansatz and the truncated Painlevé expansions. We use solutions of the two- and three-dimensional Bateman equations for the singularity manifold conditions to reduce the problem to Riccati equations. Both equations fail the Painlevé test.  相似文献   

14.
The author proposes a two-dimensional generalization of Constantin-Lax-Majda model. Some results about singular solutions are given. This model might be the first step toward the singular solutions of the Euler equations. Along the same line (vorticity formulation), the author presents some further model equations. He possibly models various aspects of difficulties related with the singular solutions of the Euler and Navier-Stokes equations. Some discussions on the possible connection between turbulence and the singular solutions of the Navier-Stokes equations are made.  相似文献   

15.
We consider the associativity or Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) equations and discuss their solution class based on the existence of the residue formulas, which is most relevant for nonperturbative physics. We demonstrate that for this case, proving the associativity equations reduces to solving a system of linear algebraic equations. Particular examples of solutions related to Landau–Ginzburg topological theories, Seiberg–Witten theories, and the tau functions of semiclassical hierarchies are discussed in detail. We also discuss related questions including the covariance of associativity equations, their relation to dispersionless Hirota relations, and the auxiliary linear problem for the WDVV equations.  相似文献   

16.
We develop a classification scheme for integrable third-order scalar evolution equations using the symmetry approach to integrability. We use this scheme to study quasilinear equations of a particular type and prove that several equations that were suspected to be integrable can be reduced to the well-known Korteweg–de Vries and Krichever–Novikov equations via a Miura-type differential substitution.  相似文献   

17.
Painlevé equations are studied on the basis of linear equations, which are generic for them. Different possible approaches are compared to each other. Formulas binding these approaches are derived. Symmetries demonstrated in the equations are also a subject of discussion.  相似文献   

18.
We establish a connection between solutions to a broad class of large systems of ordinary differential equations and solutions to retarded differential equations. We prove that solving the Cauchy problem for systems of ordinary differential equations reduces to solving the initial value problem for a retarded differential equation as the number of equations increases unboundedly. In particular, the class of systems under consideration contains a system of differential equations which arises in modeling of multiphase synthesis.  相似文献   

19.
In the paper we solve the equivalence problem of the third-order ordinary differential equations quadratic in the second-order derivative. For this class of equations the invariants of the group of point equivalence transformations and the invariant differentiation operators are constructed. Using these results the invariants of 13 Chazy equations were calculated. We provide examples of finding equivalent equations by use of their invariants. Also two new examples of the equations linearizable by a local transformation are found. These are a particular case of Chazy–XII equation and a Schwarzian equation.  相似文献   

20.
For an elliptic complex of first order differential operators on a smooth manifold X, we define a system of two equations which can be thought of as abstract Maxwell equations. The formal theory of this system proves to be very similar to that of classical Maxwell's equations. The paper focuses on boundary value problems for the abstract Maxwell equations, especially on the Cauchy problem.  相似文献   

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