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Minimality and convexity of pullback measure attractors for fractional FitzHugh-Nagumo equations with superlinear
Yangrong Li1, Xiaowen Tang1, Chunhao Qiao1
1School of Mathematics and Statistics, Southwest University, Chongqing 400715, China.
Abstract:
For a measure process, we introduce the new concept of a pullback measure attractor, which is the minimal compact invariant set and pullback attracts all norm-bounded sets of probability measures. We then establish two abstract existence theorems for pullback measure attractors. Applying to the fractional stochastic FitzHugh-Nagumo equations on an unbounded domain driven by superlinear space-time noise, we prove that the dual measure process has a minimal pullback measure attractor, which is further proved to be backward norm-bounded and convex. New methods of two-stages and direct-sum decomposition play key roles in the proofs of the continuity, forward invariance, past absorption, and pullback asymptotic tightness for the dual process.
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