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arXiv · 2412.01205

Long-time Behaviour of the Non-autonomous Stochastic FitzHugh-Nagumo Systems on Thin Domains

Dingshi Li·Ran Li·Tianhao Zeng
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Abstract

We study the long-time behavior of non-autonomous stochastic FitzHugh-Nagumo systems on thin domains. As the $(n+ 1)$-dimensional thin domains collapses onto an n-dimensional domain, an n-dimensional limiting FitzHugh-Nagumo system is derived. This n-dimensional limiting system encodes the defining geometry of the $(n+1)$-dimensional system. To justify this limiting process, we show that the pullback measure attractors of the FitzHugh-Nagumo systems on thin domains are upper semi-continuous as the height of thin direction tends to zero.

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Dingshi Li, Ran Li, Tianhao Zeng. 2024-12-02. Long-time Behaviour of the Non-autonomous Stochastic FitzHugh-Nagumo Systems on Thin Domains. https://arxiv.org/abs/2412.01205

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