LONG-TIME BEHAVIOR OF FINITE DIFFERENCE SOLUTIONS OF THREE-DIMENSIONAL NONLINEAR SCHRODINGER EQUATION WITH WEAKLY DAMPED

The three-dimensional nonlinear SchrSdinger equation with weakly damped that possesses a global attractor are considered. The dynamical properties of the discrete dynamical system which generate by a class of finite difference scheme are analysed. The existence of global attractor is proved for the discrete dynamical system.     

Finite Dimensional Behavior for Forced Nonlinear Sobolev-Galpern Equations

This paper deals with the asymptotic behavior of solutions for the nonlinear Sobolev-Galpernequations.We first show the existence of the global weak attractor in H~2(Ω)∩H_0~1(Ω) for the equations.Andthen by an energy equation we prove that the global weak attractor is actually the global strong attractor.Thefinite-dimensionality of the global attractor is also established.     

Regularity of the Attractor for the Dissipative Hamiltonian Amplitude Equation Governing Modulated Wave Instabilities

Abstract In the present paper, the existence of global attractor for dissipative Hamiltonian amplitude equationgoverning the modulated wave instabilities in E_0 is considered.By a decomposition of solution operator,it isshown that the global attractor in E_0 is actually equal to a global attractor in E_1.     

Global attractor for Hirota equation

The long time behavior of solution for Hirota equation with zero order dissipation is studied. The global weak attractor for this system in Hper^k is constructed. And then by exact analysis of the energy equation, it is shown that the global weak attractor is actually the global strong attractor in Hper^k.     

LONG-TIME BEHAVIOR OF FINITE DIFFERENCE SOLUTIONS OF THREE-DIMENSIONAL NONLINEAR SCHRDINGER EQUATION WITH WEAKLY DAMPED

The three-dimensional nonlinear Schrdinger equation with weakly damped that pos-sesses a global attractor are considered.The dynamical properties of the discrete dynamicalsystem which generate by a class of finite difference scheme are analysed.The existence ofglobal attractor is proved for the discrete dynamical system.     

ON THE EXISTENCE OF GLOBAL ATTRACTOR FOR A CLASS OF INFINITE DIMENSIONAL DISSIPATIVE NONLINEAR DYNAMICAL SYSTEMS

By means of a nonstandard estimation about the energy functional, the authors prove the existence of a global attractor for an abstract nonlinear evolution equation. As an application, the existence of a global attractor for some nonlinear reaction-diffusion equations with some distribution derivatives in inhomogeneous terms is obtained.     

Long-Time Dynamics for a Nonlinear Viscoelastic Kirchhoff Plate Equation

This paper is devoted to study the long-time dynamics for a nonlinear viscoelastic Kirchhoff plate equation. Under some growth conditions of g and f, the existence of a global attractor is granted. Furthermore, in the subcritical case, this global attractor has finite Hausdorff and fractal dimensions.     

Regularity of the attractor for 3-D complex Ginzburg-Landau equation

In this paper,the existence of global attractor for 3-D complex Ginzburg Landau equation is considered.By a decomposition of solution operator,it is shown that the global attractor A_i in H~i(Ω) is actually equal to a global attractor Aj in H~j(Ω)(i≠j,i,j = 1,2,…m).     

Exponential attractor of the 3D derivative Ginzburg-Landau equation

In this paper, we consider a derivative Ginzburg-Landau-type equation with periodic initial-value condition in three-dimensional spaces. Sufficient conditions for existence and uniqueness of a global solution are obtained by uniform a priori estimates of the solution. Furthermore, the existence of a global attractor and an exponential attractor with finite dimensions are proved.     

LONG-TIME BEHAVIOR OF FINITE DIFFERENCE SOLUTIONS OF A NONLINEAR SCHRODINGER EQUATION WITH WEAKLY DAMPED

1. IntroductionThe nonlinear schr~r equation with weakly dampedwhere t = N, o > 0, together with appropriate boUndary and hatal condition, is ared inmany physical fields. The echtence of an attractor is one of the most boortant ~eristiCSfor a dissipative system. The long-tabs dynamics is completely determined by the attractorof the system. J.M. Ghidaglia[1] studied the lOng-the behavior of the nonlineaz Sequation (1.1) and proved the eAstence of a compact global attractor A in H'(n) which…     

Random attractor for a two-dimensional incompressible non-Newtonian fluid with multiplicative noise

This article proves that the random dynamical system generated by a twodimensional incompressible non-Newtonian fluid with multiplicative noise has a global random attractor, which is a random compact set absorbing any bounded nonrandom subset of the phase space.     

The existence of global attractors for 2D Navier-Stokes equations in <Emphasis Type="Italic">H</Emphasis><Superscript><Emphasis Type="Italic">k</Emphasis></Superscript> spaces

In this paper, we prove that the 2D Navier-Stokes equations possess a global attractor in Hk（Ω,R2） for any k ≥ 1, which attracts any bounded set of Hk（Ω,R2） in the H^k-norm. The result is established by means of an iteration technique and regularity estimates for the linear semigroup of operator, together with a classical existence theorem of global attractor. This extends Ma, Wang and Zhong＇s conclusion.     

GLOBAL ATTRACTIVITY OF A DIFFERENCE EQUATION

In this paper,we investigate the global stability of all positive solutions to a difference equation.We show that the unique positive equilibrium of the equation is a global attractor with a basin under some certain conditions on the coefficient.     

Attractor for lattice system of dissipative Zakharov equation

We consider the asymptotic behavior of solutions of an infinite lattice dynamical system of dissipative Zakharov equation. By introducing new weight inner product and norm in the space and establishing uniform estimate on ＂Tail End＂ of solutions, we overcome some difficulties caused by the lack of Sobolev compact embedding under infinite lattice system, and prove the existence of the global attractor; then by using element decomposition and the covering property of a polyhedron in the finite-dimensional space, we obtain an upper bound for the Kolmogorov ε-entropy of the global attractor; finally, we present the upper semicontinuity of the global attractor.     

Finite dimensional global and exponential attractors for a class of coupled time-dependent Ginzburg-Landau equations

We study a coupled nonlinear evolution system arising from the Ginzburg-Landau theory for atomic Fermi gases near the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover.First,we prove that the initial boundary value problem generates a strongly continuous semigroup on a suitable phase-space which possesses a global attractor.Then we establish the existence of an exponential attractor.As a consequence,we show that the global attractor is of finite fractal dimension.     

Long-time Dynamics for Thermoelastic Bresse System of Type Ⅲ

This paper considers the thermoelastic beam system of type Ⅲ with friction dissipations acting on the whole system. By using the methods developed by Chueshov and Lasiecka, we get the quasi-stability property of the system and obtain the existence of a global attractor with finite fractal dimension. Result on exponential attractors of the system is also proved.     

一个四阶方程组在全直线上的整体吸引子

This paper studies the long time behavior of the following Cauchy problem The authors prove the existence of global attractor by showing the corresponding operator semigroup is asymptotically compact.     

LONG-TIME DYNAMICS OF THE STRONGLY DAMPED SEMILINEAR PLATE EQUATION IN R~N

We investigate the initial-value problem for the semilinear plate equation containing localized strong damping, localized weak damping and nonlocal nonlinearity. We prove that if nonnegative damping coefficients are strictly positive almost everywhere in the exterior of some ball and the sum of these coefficients is positive a.e. in R~n, then the semigroup generated by the considered problem possesses a global attractor in H~2(R~n) × L~2(R~n).We also establish the boundedness of this attractor in H~3(R~n) × H~2(R~n).     

GLOBAL BEHAVIOR IN A RATIONAL RECURSIVE SEQUENCE

In this paper, we study the global stability, and the periodic character of the rational recursive sequence. We show that the positive equilibrium of the sequence is a global attractor with a basin which depends on certain conditions posed on the coefficients.     

平面不可压缩的Navier-Stokes方程的一个新七模截断(英文)

A new seven-modes truncation of Fourier series of Navier-Stokes equations for a two-dimensional incompressible fluid on a torus is obtained.And its stationary solutions,the existence of attractor and the global stability of the equations are firmly proved.At the same time,several issues such as some basic dynamical behaviors and routs to chaos are shown numerically by changing Reynolds number.The system exhibits a stochastic behavior approached through an involved sequence of bifurcations.