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arXiv · 1504.04153

Regularity of pullback attractors and equilibria for a stochastic non-autonomous reaction-diffusion equations perturbed by a multiplicative noise

Wenqiang Zhao·Shuzhi Song
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Abstract

In this paper, a standard about the existence and upper semi-continuity of pullback attractors in the non-initial space is established for some classes of non-autonomous SPDE. This pullback attractor, which is the omega-limit set of the absorbing set constructed in the initial space, is completely determined by the asymptotic compactness of solutions in both the initial and non-initial spaces. As applications, the existences and upper semi-continuity of pullback attractors in $H^1(\mathbb{R}^N)$ are proved for stochastic non-autonomous reaction-diffusion equation driven by a multiplicative noise. Finally we show that under some additional conditions the cocycle admits a unique equilibrium.

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Wenqiang Zhao, Shuzhi Song. 2015-04-16. Regularity of pullback attractors and equilibria for a stochastic non-autonomous reaction-diffusion equations perturbed by a multiplicative noise. https://arxiv.org/abs/1504.04153

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