Well-posedness and dynamics of fractional Fitz Hugh-Nagumo systems on R^(N) driven by nonlinear noise

作     者：Renhai Wang Boling Guo Bixiang Wang Renhai Wang;Boling Guo;Bixiang Wang

作者机构：Institute of Applied Physics and Computational MathematicsBeijing 100088China Department of MathematicsNew Mexico Institute of Mining and TechnologySocorroNM 87801USA 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2021年第64卷第11期

页      面：2395-2436页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 071101[理学-系统理论] 

基　　金：supported by the China Scholarship Council(Grant No.201806990064) 

主　　题：fractional Fitz Hugh-Nagumo system weak pullback mean random attractor invariant measure nonlinear noise unbounded domain 

摘      要：This article is concerned with the well-posedness as well as long-term dynamics of a wide class of non-autonomous,non-local,fractional,stochastic Fitz Hugh-Nagumo systems driven by nonlinear noise defined on the entire space *** well-posedness is proved for the systems with polynomial drift terms of arbitrary order as well as locally Lipschitz nonlinear diffusion terms by utilizing the pathwise and mean square uniform *** mean random dynamical system generated by the solution operators is proved to possess a unique weak pullback mean random attractor in a Bochner *** existence of invariant measures is also established for the autonomous systems with globally Lipschitz continuous diffusion *** idea of uniform tail-estimates of the solutions in the appropriate spaces is employed to derive the tightness of a family of probability distributions of the solutions in order to overcome the non-compactness of the standard Sobolev embeddings on RNas well as the lack of smoothing effect on one component of the *** results of this paper are new even when the fractional Laplacian is replaced by the standard Laplacian.