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Dynamics of stochastic FitzHugh-Nagumo systems with additive noise on unbounded thin domains. (English) Zbl 1439.35592

Summary: We investigate the asymptotic behavior of a class of non-autonomous stochastic FitzHugh-Nagumo systems driven by additive white noise on unbounded thin domains. For this aim, we first show the existence and uniqueness of random attractors for the considered equations and their limit equations. Then, we establish the upper semicontinuity of these attractors when the thin domains collapse into a lower-dimensional unbounded domain.

MSC:

35R60 PDEs with randomness, stochastic partial differential equations
35B40 Asymptotic behavior of solutions to PDEs
35B41 Attractors
37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
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