Citation: | Yanjiao Li, Xiaojun Li, Jiabin Zuo. RANDOM ATTRACTORS FOR NON-AUTONOMOUS STOCHASTIC WAVE EQUATIONS WITH STRONG DAMPING AND ADDITIVE NOISE ON $ {\mathbb{R}}^{N} $[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 1739-1765. doi: 10.11948/20220006 |
This paper investigates the long-time behavior of a stochastic strongly damped wave equation with additive noise on $ \mathbb{R}^{N} $. We establish that there exists a unique pullback random attractor for the equation in space $ H^1( {\mathbb{R}}^{N})\times L^2( {\mathbb{R}}^{N}) $ with the nonlinearity $ g(x,u) $ being of optimal subcritical growth $ p $: $ 1\leq p <p^*\equiv\frac{N+2}{(N-2)}(N\geq 3) $. In addition, we get the upper semicontinuity of the pullback random attractor as the intensity of noise goes to zero.
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