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 entir...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 RN.The 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 estimates.The mean random dynamical system generated by the solution operators is proved to possess a unique weak pullback mean random attractor in a Bochner space.The existence of invariant measures is also established for the autonomous systems with globally Lipschitz continuous diffusion terms.The 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 solutions.The results of this paper are new even when the fractional Laplacian is replaced by the standard Laplacian.展开更多
基金supported by the China Scholarship Council(Grant No.201806990064)。
文摘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 RN.The 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 estimates.The mean random dynamical system generated by the solution operators is proved to possess a unique weak pullback mean random attractor in a Bochner space.The existence of invariant measures is also established for the autonomous systems with globally Lipschitz continuous diffusion terms.The 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 solutions.The results of this paper are new even when the fractional Laplacian is replaced by the standard Laplacian.
