非线性应变波耦合组的吸引子的正则性

本文研究了非线性应变波方程与Schr(?)dinger方程耦合系统Cauchy问题吸引 子的正则性.获得了该系统在空间Eo中存在整体吸引子Ao,并且Ao与E1中的强吸 引子A1相等.     

Dynamical system generated by the equations of motion of an Oldroyd fluid of order L

The attractor m and dynamical system {m;V_t,–相似文献   

Finite dimensionality of global attractors for a non-classical reaction-diffusion equation with memory

In this paper, we consider a periodic boundary value problem for a non-classical reaction-diffusion equation with memory. In other paper, we use the ω-limit compactness of the solution semigroup {S(t)}_t≥0 to get the existence of a global attractor. The main goal here is to give an estimate of the fractal dimension of the global attractor. By the fractal dimension theorem given by A.O. Celebi et al., we obtain that the fractal dimension of the global attractor for the problem is finite; this makes the results for the non-classical reaction-diffusion equations more substantial and perfect.     

Dynamical system generated by the equations of motion of Oldroyd fluids

An attractor m is constructed for the two-dimensional initial-boundary problem for the equations of motion of Oldroyd's fluid, the properties of the evolution operator V_t, t0, are investigated, and the dynamical system {m; V_t, –t} is constructed.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 136–141, 1986.The authors express gratitude to L. D. Faddeev and O. A. Ladyzhenskava for supporting their research on the hydrodynamics of non-Newtonian fluids.     

Properties of the attractor in the problem of the nonlinear oscillations of an infinite panel

In the problem of the nonlinear oscillations of an infinite panel in a supersonic gas flow, the existence of a maximal attractor and the finiteness of its fractal dimension are proved. The dimension is estimated from above in terms of the parameters of the problem. Cases are indicated when the attractor has a regular structure.Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 50, pp. 108–115, 1988.     

Pullback attractors for a class of extremal solutions of the 3D Navier-Stokes system

In this paper we construct a dynamical process (in general, multivalued) generated by the set of solutions of an optimal control problem for the three-dimensional Navier-Stokes system. We prove the existence of a pullback attractor for such multivalued process. Also, we establish the existence of a uniform global attractor containing the pullback attractor. Moreover, under the unproved assumption that strong globally defined solutions of the three-dimensional Navier-Stokes system exist, which guaranties the existence of a global attractor for the corresponding multivalued semiflow, we show that the pullback attractor of the process coincides with the global attractor of the semiflow.     

An improved training algorithm for feedforward neural network learning based on terminal attractors

In this paper, an improved training algorithm based on the terminal attractor concept for feedforward neural network learning is proposed. A condition to avoid the singularity problem is proposed. The effectiveness of the proposed algorithm is evaluated by various simulation results for a function approximation problem and a stock market index prediction problem. It is shown that the terminal attractor based training algorithm performs consistently in comparison with other existing training algorithms.     

Attractors of Navier-Stokes systems and of parabolic equations,and estimates for their dimensions

One investigates the problem of the existence of an attractor α of the semi-group S_t, generated by the solutions of the nonlinear nonstationary equations $$\frac{{\partial u}}{{\partial t}} = A(u), u|_{t = 0} = u_0 (x); S_t u_0 \equiv u(t)$$ . One proves a very general theorem on the existence of an attractor α of the semigroup S_t for t→∞. One gives examples of differential equations having attractors: a second-order quasilinear parabolic equation, a two-dimensional Navier—Stokes system, a monotone parabolic equation of any order. One proves a theorem on the finiteness of the Hausdorff dimension of the attractor α. One gives an estimate for the Hausdorff dimension of the attractor α for a two-dimensional Navier—Stokes system.     

非自治半线性热黏弹性问题的一致吸引子的维数(英文)

In this paper, we prove the existence of a uniform attractor for the process associated with a non-antonomous semilinear thermoelastic problem. And under the certain parameter, we obtain an upper bound for the Hausdorff dimension of the uniform attractor.     

Global Solutions and Their Large-time Behavior of Cauchy Problem for Equations of Deep Water Type

We consider the large time behavior of the global solution of the Cauchy problem for the equation of Benjamin-Ono type. A series of large-time global estimates for Cauchy problem arc constructed. By means of the obtained global estimates uniformly for 0 ≤ t < ∞, the attractors of the Cauchy problem for the mentioned nonlinear equations are considered. And also the dimensions of the global attractor are estimated.     

一类长短波方程组的整体吸引子的存在性(英)

本文应用对时间的一致先验估计,证明了一类具有周期边值条件的长短波方程组的整体吸引子的存在性．     

Weak solutions and attractors for motion equations for an objective model of viscoelastic medium

We study the boundary value problem for the equations of motion of incompressible viscoelastic medium with an objective constitutive law of Jeffreys kind. We show existence of global weak solutions for any initial data and construct their minimal uniform trajectory attractor and uniform global attractor. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Seeking global edges for traveling salesman problem in multi-start search

This study investigates the properties of the edges in a set of locally optimal tours found by multi-start search algorithm for the traveling salesman problem (TSP). A matrix data structure is used to collect global information about edges from the set of locally optimal tours and to identify globally superior edges for the problem. The properties of these edges are analyzed. Based on these globally superior edges, a solution attractor is formed in the data matrix. The solution attractor is a small region of the solution space, which contains the most promising solutions. Then an exhausted enumeration process searches the solution attractor and outputs all solutions in the attractor, including the globally optimal solution. Using this strategy, this study develops a procedure to tackler a multi-objective TSP. This procedure not only generates a set of Pareto-optimal solutions, but also be able to provide the structural information about each of the solutions that will allow a decision-maker to choose the best compromise solution.     

Hasegawa-Mima方程的整体吸引子

考虑了带有耗散项的Hasegawa-Mima方程解的长时间性态, 研究了具有初值周期边值条件的Hasegawa-Mima方程的整体吸引子问题．运用关于时间的一致先验估计,证明了该问题整体吸引子的存在性,并获得了整体吸引子的维数估计．     

Approximate inertial manifolds for the 2d model of atmosphere

In order to understand the mechanism of long term weather prediction and climate, we construct explicitly in this paper an infinite number of approximate inertial manifolds M _j,m for the 2D model of large scale atmosphere to approximate the global attractor of the model. Associated with each manifold, there exists a thin neighborhood of it, into which the orbits of the model enter with a finite time. These neighborhoods contain and localize the global attractor. The thickness of these neighborhoods decreases with increasing m for a fixed j. Moreover we also obtain the time analyticity of the solutions of the model and the behavior of the small structures.     

Dynamics of Thermally-Insulated Nonequilibrium Stefan Problem

We study a two-phase Stefan problem with kinetics. Here we prove existence of a finite-dimensional attractor for the problem without heat losses. Fot the most part we use a more elegant technique of energetic type estimates in appropriately defined weighted Sobolev spaces as opposite to the parabolic potentials of [9]. We demonstrate existence of compact attractors in the Sobolev spaces and prove that the attractor consists of sufficiently regular functions. This allows us to show that the Hausdorff dimension of the attractor is finite.     

Global attractor for heat convection problem in a micropolar fluid

The article is devoted to describe asymptotics in the heat convection problem for a micropolar fluid in two dimensions. We show the existence and the uniqueness of global in time solutions and then prove the existence of a global attractor for considered model. Next, the Hausdorff dimension of the global attractor is estimated. Copyright © 2006 John Wiley & Sons, Ltd.     

DYNAMIC BIFURCATION OF NONLINEAR EVOLUTION EQUATIONS

§1. IntroductionA key problem in the study of problems in mathematical physics and mechanics is tounderstand and predict patterns and their transitions/evolutions. In ?uid mechanics, forinstance, it is important to study the periodic, quasi-periodic, ape…     

Attractor dimension estimate for plane shear flow of micropolar fluid with free boundary

This research is motivated by a problem from lubrication theory. We consider a free boundary problem of a two‐dimensional boundary‐driven micropolar fluid flow. The existence of a unique global‐in‐time solution of the problem and the global attractor for the associated semigroup are known. In this paper we estimate the dimension of the global attractor in terms of the given data and the geometry of the domain of the flow by establishing a new version of the Lieb–Thirring inequality with constants depending explicitly on the geometry of the domain. We also obtain some new estimates for the Navier–Stokes shear flows. Copyright © 2005 John Wiley & Sons, Ltd.     

Homoclinical structure of the chaotic attractor

In the reference [Akhmet MU. Devaney chaos of a relay system. Commun Nonlinear Sci Numer Simulat 2009;14:1486–93.], a relay system was introduced, which admits a chaotic attractor with Devaney’s ingredients. Now, we prove that the attractor consists of homoclinic solutions. A simulation of the attractor is provided for a pendulum equation. Similar results for impulsive differential equations were announced in the plenary talk [Akhmet MU. Hyperbolic sets of impact systems. Dyn Contin Discrete Impuls Syst Ser A Math Anal 2008;15(Suppl. S1):1–2. Proceedings of the 5th international conference on impulsive and hybrid dynamical systems and applications, Beijin: Watan Press; 2008.].