Author:
Duc Luu Hoang,Hong Phan Thanh
Abstract
AbstractWe provide a unified analytic approach to study the asymptotic dynamics of Young differential equations, using the framework of random dynamical systems and random attractors. Our method helps to generalize recent results (Duc et al. in J Differ Equ 264:1119–1145, 2018, SIAM J Control Optim 57(4):3046–3071, 2019; Garrido-Atienza et al. in Int J Bifurc Chaos 20(9):2761–2782, 2010) on the existence of the global pullback attractors for the generated random dynamical systems. We also prove sufficient conditions for the attractor to be a singleton, thus the pathwise convergence is in both pullback and forward senses.
Funder
Max Planck Institute for Mathematics in the Sciences
Publisher
Springer Science and Business Media LLC
Reference25 articles.
1. Adrianova, L.Y.: Introduction to linear systems of differential equations. In: Translations of Mathematical Monographs, vol. 46, Americal Mathematical Society (1995)
2. Amann, H.: Ordinary Differential Equations: An Introduction to Nonlinear Analysis. Walter de Gruyter, Berlin (1990)
3. Arnold, L.: Random Dynamical Systems. Springer, Berlin (1998)
4. Bailleul, I., Riedel, S., Scheutzow, M.: Random dynamical systems, rough paths and rough flows. J. Differ. Equ. 262, 5792–5823 (2017)
5. Cass, T., Litterer, C., Lyons, T.: Integrability and tail estimates for Gaussian rough differential equations. Ann. Probab. 14(4), 3026–3050 (2013)
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献