Upper Semicontinuity Of Random Attractors Research Articles

Asymptotic behavior of non-autonomous fractional stochastic reaction–diffusion equations

We first apply the Galerkin method to prove the existence and uniqueness of solutions for a class of non-autonomous fractional reaction–diffusion equations driven by multiplicative noise. We then establish the existence and uniqueness of tempered pullback random attractors for the equations in an appropriate Hilbert space. The upper semicontinuity of random attractors is also obtained when the intensity of noise approaches zero.

Existence and upper semicontinuity of random attractors for non-autonomous stochastic strongly damped sine–Gordon equation on unbounded domains

In this paper we study the asymptotic behavior of solutions of the non-autonomous stochastic strongly damped sine–Gordon equation driven by multiplicative noise defined on an unbounded domain. First we introduce a continuous cocycle for the equation and establish the pullback asymptotic compactness of solutions. Second we consider the existence and upper semicontinuity of random attractors for the equation.

A Combined Criterion for Existence and Continuity of Random Attractors for Stochastic Lattice Dynamical Systems

The paper is devoted to establishing a combination of sufficient criterion for the existence and upper semi-continuity of random attractors for stochastic lattice dynamical systems. By relying on a family of random systems itself, we first set up the abstract result when it is convergent, uniformly absorbing and uniformly random when asymptotically null in the phase space. Then we apply the results to the second-order lattice dynamical system driven by multiplicative white noise. It is indicated that the criterion depending on the dynamical system itself seems more applicable than the existing ones to lattice differential models.

Existence and upper semicontinuity of random attractors for non-autonomous stochastic strongly damped wave equation with multiplicative noise

In this paper we study the asymptotic behavior of solutions of the non-autonomous stochastic strongly damped wave equation driven by multiplicative noise defined on unbounded domains. We first introduce a continuous cocycle for the equation. Then we consider the existence of a tempered pullback random attractor for the cocycle. Finally we establish the upper semicontinuity of random attractors as the coefficient of the white noise term tends to zero.

Upper semicontinuity of random attractors for the stochastic non-autonomous suspension bridge equation with memory

This paper is devoted to the well-posedness and long-time behavior of a stochastic suspension bridge equation with memory effect. The existence of the random attractor for the stochastic suspension bridge equation with memory is established. Moreover, the upper semicontinuity of random attractors is also provided when the coefficient of random term approaches zero.

Wong-Zakai approximations and asymptotic behavior of stochastic Ginzburg-Landau equations

In this paper we discuss the Wong-Zakai approximations given by a stationary process via the Wiener shift and their associated long term pathwise behavior for stochastic Ginzburg-Landau equations driven by a white noise. We first apply the Galerkin method and compactness argument to prove the existence and uniqueness of weak solutions. Consequently, we show that the approximate equation has a pullback random attractor under much weaker conditions than the original stochastic equation. At last, when the stochastic Ginzburg-Landau equation is driven by a linear multiplicative noise, we establish the convergence of solutions of Wong-Zakai approximations and the upper semicontinuity of random attractors of the approximate random system as the size of approximation approaches zero.

Existence and upper semicontinuity of attractors for non-autonomous stochastic lattice FitzHugh-Nagumo systems in weighted spaces

In this paper, we first consider the existence of random attractors for the non-autonomous stochastic lattice FitzHugh-Nagumo system with random coupled coefficients and additive white noise in a weighted space $l_{\rho }^{2} \times l_{\rho }^{2} $ ; then we establish the upper semicontinuity of random attractors as the intensity of noise approaches zero.

Random Attractor Associated with the Quasi-Geostrophic Equation

We study the long time behavior of the solutions to the 2D stochastic quasi-geostrophic equation on $\mathbb{T}^2$ driven by additive noise and real linear multiplicative noise in the subcritical case (i.e. $\alpha>1/2$) by proving the existence of a random attractor. The key point for the proof is the exponential decay of the $L^p$-norm and a boot-strapping argument. The upper semicontinuity of random attractors is also established. Moreover, if the viscosity constant is large enough, the system has a trivial random attractor.

Random Attractors for Non-autonomous Stochastic Lattice FitzHugh-Nagumo Systems with Random Coupled Coefficients

In this paper, we study the non-autonomous stochastic lattice FitzHugh-Nagumo system with random coupled coefficients and multiplicative white noise. We consider the existence of random attractors in a weighted space $l_\rho^2 \times l_\rho^2$ for this system, and establish the upper semicontinuity of random attractors as the intensity of noise approaches zero.

Existence and Upper Semicontinuity of Attractors for Nonautonomous Stochastic Sine-Gordon Lattice Systems with Random Coupled Coefficients

We study nonautonomous stochastic sine-Gordon lattice systems with random coupled coefficients and multiplicative white noise. We first consider the existence of random attractors in a weighted space for this system and then establish the upper semicontinuity of random attractors as the intensity of noise approaches zero.

Existence and upper semicontinuity of random attractors for stochastic degenerate parabolic equations with multiplicative noises

The existence and the upper semicontinuity of random attractors in L2(RN) for stochastic semi-linear degenerate parabolic equations with multiplicative noises are obtained. Though the spatial domain is the entire space RN, a compact embedding is applied to get the compactness of random absorbing sets, from which follows the compactness of the system and the precompactness of the union of all perturbed random attractors.

Random attractor of non-autonomous stochastic Boussinesq lattice system

In this paper, we first consider the existence of tempered random attractor for second-order non-autonomous stochastic lattice dynamical system of nonlinear Boussinesq equations effected by time-dependent coupled coefficients and deterministic forces and multiplicative white noise. Then, we establish the upper semicontinuity of random attractors as the intensity of noise approaches zero.

Random attractors for damped non-autonomous wave equations with memory and white noise

We first prove the existence of random attractors for the continuous random dynamical systems generated by stochastic damped non-autonomous wave equations with linear memory and additive white noise when the nonlinearity has a critically growing exponent. Then we study the upper semicontinuity of random attractors when the coefficient of random term approaches zero.

Attractors of non-autonomous stochastic lattice systems in weighted spaces

We study the asymptotic behavior of solutions to a class of non-autonomous stochastic lattice systems driven by multiplicative white noise. We prove the existence and uniqueness of tempered random attractors in a weighted space containing all bounded sequences, and establish the upper semicontinuity of random attractors as the intensity of noise approaches zero. We also construct maximal and minimal tempered random complete solutions which bound the attractors from above and below, respectively. When deterministic external forcing terms are periodic in time, we show the random attractors are pathwise periodic. In addition, we exhibit a non-autonomous stochastic lattice system which possesses an infinite-dimensional tempered random attractor.

Upper semicontinuity of random attractors for stochastic three-component reversible Gray–Scott system

We consider the upper semicontinuity of the global random attractors for the stochastic three-component reversible Gray–Scott system on unbounded domains when the intensity of the noise converges to zero.

A random attractor for a stochastic second order lattice system with random coupled coefficients

In this paper, we mainly focus on the asymptotic behavior of solutions to the second-order stochastic lattice equations with random coupled coefficients and multiplicative white noises in weighted spaces of infinite sequences. We first transfer stochastic lattice equations into random lattice equations and prove the existence and uniqueness of solutions which generate a random dynamical system. Second we consider the existence of a tempered random bounded absorbing set and a random attractor for the system. Then we establish the upper semicontinuity of random attractors as the coefficient of the white noise term tends to zero. Finally we present the corresponding results for the system with additive white noises.

Upper-semicontinuity of attractors for random lattice systems perturbed by small white noises

In this paper, we first present some conditions for the upper semicontinuity of perturbed random attractors to a limiting random attractor. Then we apply this result to establish the upper semicontinuity of random attractors for the first order stochastic lattice differential equations with random coupled coefficients and multiplicative/additive white noises in the weighted space of infinite sequences as the coefficient of the white noise term tends to zero.