Abstract
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.
Highlights
We study nonautonomous stochastic sine-Gordon lattice systems with random coupled coefficients and multiplicative white noise
Stochastic lattice differential equations arise naturally in a wide variety of applications where the spatial structure has a discrete character and uncertainties are taken into account
Some works have been done regarding the existence of random attractors for stochastic lattice differential equations
Summary
Stochastic lattice differential equations arise naturally in a wide variety of applications where the spatial structure has a discrete character and uncertainties are taken into account. Zhou and Wei [11] considered the existence of random attractors for second-order lattice system with random coupled coefficients and multiplicative white noise. Motivated by [2, 11], we will study the asymptotic behavior of solutions of the following nonautonomous stochastic sineGordon lattice systems with random coupled coefficients and multiplicative white noise: for every τ ∈ R and t > τ, d2ui dt. To the best of our knowledge, there are no results on nonautonomous stochastic sine-Gordon lattice systems with random coupled coefficients and multiplicative white noise. We first consider the existence of a tempered random attractor in a weighted space lρ2 × lρ for stochastic. Discrete Dynamics in Nature and Society sine-Gordon lattice systems (1), which attracts the random tempered bounded sets in pullback sense.
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