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Abstract
This paper is devoted to the convergence of bi-spatial random attractors as a family of bounded domains is extended to be unbounded. Some criteria in terms of expansion and restriction are provided to ensure that the unbounded-domain attractor is approximated by the family of bounded-domain attractors in both upper and lower semi-continuity senses. The theoretical results are applied to show that the stochastic FitzHugh–Nagumo coupled equations have an attractor in [Formula: see text]-times Lebesgue space irrespective of whether the domain is bounded or unbounded. Furthermore, we prove that the family of bounded-domain attractors continuously converges to the unbounded-domain attractor, and the latter can be constructed by the metric-limit set of all bounded-domain attractors.
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Affiliation(s)
- Yangrong Li
- School of Mathematics and Statistics, Southwest University, Chongqing 400715, P. R. China
| | - Fuzhi Li
- School of Mathematics and Statistics, Southwest University, Chongqing 400715, P. R. China
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