Dynamics for stochastic Fitzhugh–Nagumo systems with general multiplicative noise on thin domains

Abstract

This paper is devoted to studying the dynamics for stochastic Fitzhugh–Nagumo equations with general multiplicative noise on thin domains, where the noise is described by a general stochastic process instead of the usual Wiener process. The measurability of the solution operator is proved, which yields to the measurability of the random attractor. We then show the existence and upper semi‐continuity of these attractors when a family of (n + 1)‐dimensional thin domains degenerates onto an n‐dimensional domain under the topology of p‐times Lebesgue space.