DCDS
Random attractor for stochastic non-autonomous damped wave equation with critical exponent
Zhaojuan Wang Shengfan Zhou

In this paper, we prove the existence of random attractor and obtainan upper bound of fractal dimension of random attractor forstochastic non-autonomous damped wave equation with criticalexponent and additive white noise. We first prove the existence of arandom attractor by carefully splitting the positivity of the linearoperator in the corresponding random evolution equation of the firstorder in time and by carefully decomposing the solutions of systemthrough two different modes, and we show the boundedness of randomattractor in a higher regular space by a recurrence method. Then weestablish a criterion to bound the fractal dimension of a randominvariant set for a cocycle and applied these conditions to get anupper bound of fractal dimension of the random attractor ofconsidered system.

keywords: Stochastic damped wave equation random attractor fractal dimension critical exponent
DCDS
Existence and upper semicontinuity of random attractors for non-autonomous stochastic strongly damped wave equation with multiplicative noise
Zhaojuan Wang Shengfan Zhou

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.

keywords: Stochastic strongly damped wave equation unbounded domains random attractor upper semicontinuity
CPAA
Existence and upper semicontinuity of attractors for non-autonomous stochastic lattice systems with random coupled coefficients
Zhaojuan Wang Shengfan Zhou
In this paper, we consider the existence of random attractors in a weighted space $ l_\rho ^2 $ for first-order non-autonomous stochastic lattice system with random coupled coefficients and multiplicative/additive white noise, and establish the upper semicontinuity of random attractors as the intensity of noise approaches zero.
keywords: Non-autonomous stochastic lattice dynamical system random attractor random coupled coefficient.

Year of publication

Related Authors

Related Keywords

[Back to Top]