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1.
In this paper, we consider a lattice system of stochastic Zakharov equation with white noise. We first show that the solutions of the system determine a continuous random dynamical system with random absorbing set. And then we prove the random asymptotic compact on the random absorbing set. Finally, we obtain the existence of a random attractor for the system. 相似文献
2.
Xiaolin Xiang 《Journal of Difference Equations and Applications》2016,22(2):235-252
In this paper, we consider the asymptotic behaviour of solutions to second-order non-autonomous stochastic lattice equations with dispersive term and additive white noises in the space of infinite sequences. We first transfer the stochastic lattice equations into random lattice equations, and prove the existence and uniqueness of solutions that generate a random dynamical system. Second, we prove the existence of a tempered random absorbing set and a random attractor for the system. Finally, we establish the upper semi-continuity of the random attractors as the coefficient of the white noise term tends to zero. 相似文献
3.
The aim of this article is to study the asymptotical behavior, in terms of upper semi-continuous property of attractor, for small multiplicative noise of the three-dimensional planetary geostrophic equations of large-scale ocean circulation. In this article, we establish the existence of a random attractor for the three-dimensional planetary geostrophic equations of large-scale ocean circulation with small multiplicative noise by verifying the pullback flattening property and prove that the random attractor of the three-dimensional planetary geostrophic equations of large-scale ocean circulation with small multiplicative noise converges to the global attractor of the unperturbed three-dimensional planetary geostrophic equations of large-scale ocean circulation when the parameter of the perturbation tends to zero. 相似文献
4.
Tomás CARABALLO 《Frontiers of Mathematics in China》2008,3(3):317-335
In this paper, we consider a stochastic lattice differential equation with diffusive nearest neighbor interaction, a dissipative
nonlinear reaction term, and multiplicative white noise at each node. We prove the existence of a compact global random attractor
which, pulled back, attracts tempered random bounded sets.
相似文献
5.
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. 相似文献
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7.
Xiaoying Han 《Journal of Mathematical Analysis and Applications》2011,376(2):481-493
We study the asymptotic behavior of solutions to the stochastic sine-Gordon lattice equations with multiplicative white noise. We first prove the existence and uniqueness of solutions, and then establish the existence of tempered random bounded absorbing sets and global random attractors. 相似文献
8.
We study the random dynamical system (RDS) generated by the Benald flow problem with multiplicative noise and prove the existence of a compact random attractor for such RDS. 相似文献
9.
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. 相似文献
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Zhaojuan Wang 《Journal of Mathematical Analysis and Applications》2011,384(1):160-172
In this paper we study the asymptotic dynamics for stochastic reaction-diffusion equation with multiplicative noise defined on unbounded domains. We investigate the existence of a random attractor for the random dynamical system associated with the equation. The asymptotic compactness of the random dynamical system is established by using uniform a priori estimates for far-field values of solutions and a cut-off technique. 相似文献
12.
Random attractors for stochastic reaction‐diffusion equations with multiplicative noise in 下载免费PDF全文
Yanbin Tang 《Mathematische Nachrichten》2014,287(14-15):1774-1791
In this paper, we study the random dynamical system generated by a stochastic reaction‐diffusion equation with multiplicative noise and prove the existence of an ‐random attractor for such a random dynamical system. The nonlinearity f is supposed to satisfy some growth of arbitrary order . 相似文献
13.
This paper studies the dynamical behavior of the Ladyzhenskaya model with additive noise. With some conditions, we prove that the generated random dynamical system has a compact random attractor, which is a random compact set absorbing any bounded nonrandom subset of the phase space. 相似文献
14.
Wong-Zakai approximations and attractors for fractional stochastic reaction-diffusion equations on unbounded domains 下载免费PDF全文
In this paper, we investigate the Wong-Zakai approximations induced by a stationary process and the long term behavior of the fractional stochastic reaction-diffusion equation driven by a white noise. Precisely, one of the main ingredients in this paper is to establish the existence and uniqueness of tempered pullback attractors for the Wong-Zakai approximations of fractional stochastic reaction-diffusion equations. Thereafter the upper semi-continuity of attractors for the Wong-Zakai approximation of the equation as $\delta\rightarrow0$ is proved. 相似文献
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16.
T. Sasagawa 《Journal of Optimization Theory and Applications》1989,61(3):451-471
For the deterministic case, a linear controlled system is alwayspth order stable as long as we use the control obtained as the solution of the so-called LQ-problem. For the stochastic case, however, a linear controlled system with multiplicative noise is not alwayspth mean stable for largep, even if we use the LQ-optimal control. Hence, it is meaningful to solve the LP-optimal control problem (i.e., linear system,pth order cost functional) for eachp. In this paper, we define the LP-optimal control problem and completely solve it for the scalar case. For the multidimensional case, we get some results, but the general solution of this problem seems to be impossible. So, we consider thepth mean stabilization problem more intensively and give a sufficient condition for the existence of apth mean stabilizing control by using the contraction mapping method in a Hilbert space. Some examples are also given.This research was conducted while the author was a visitor at the Forschungsschwerpunkt Dynamische Systeme, Universität Bremen, Bremen, West Germany. The author is grateful to Professor L. Arnold for providing interesting seminars and excellent working conditions during his stay. The financial assistance given by the Alexander von Humboldt Foundation during the author's stay is also gratefully acknowledged. 相似文献
17.
We study the ill-posedness question for the one-dimensional Zakharov system and a generalization of it in one and higher dimensions. Our point of reference is the criticality criteria introduced by Ginibre, Tsutsumi and Velo (1997) to establish local well-posedness.
18.
Random attractors for non-autonomous fractional stochastic Ginzburg-Landau equations on unbounded domains 下载免费PDF全文
This paper deals with the dynamical behavior of solutions for non-autonomous stochastic fractional Ginzburg-Landau equations driven by additive noise with $\alpha\in(0,1)$. We prove the existence and uniqueness of tempered pullback random attractors for the equations in $L^{2}(\mathbf{R}^{3})$. In addition, we also obtain the upper semicontinuity of random attractors when the intensity of noise approaches zero. The main difficulty here is the noncompactness of Sobolev embeddings on unbounded domains. To solve this, we establish the pullback asymptotic compactness of solutions in $L^{2}(\mathbf{R}^{3})$ by the tail-estimates of solutions. 相似文献
19.
Fractal Dimension of Random Attractors for Non-autonomous Fractional Stochastic Reaction-diffusion Equations 下载免费PDF全文
This paper dealswith non-autonomous fractional stochastic reaction-diffusion equations driven by multiplicative noise with s ∈ (0,1). We first present some conditions for estimating the boundedness of fractal dimension of a random invariant set. Then we establish the existence and uniqueness of tempered pullback random attractors. Finally, the finiteness of fractal dimension of the random attractors is proved. 相似文献
20.
In this paper,we consider the existence of a uniform exponential attractor for the nonautonomous partly dissipative lattice dynamical system with quasiperiodic external forces. 相似文献