报告人：王碧祥
报告题目：Dynamics of Stochastic Reaction-Diffusion Equations Driven by Nonlinear Noise
摘要:This talk is concerned with the asymptotic behavior of the solutions of the fractional reaction-diffusion equations with polynomial drift terms of arbitrary order driven by nonlinear discusion terms defined on unbounded domains. We first discuss the well-posedness of the equations and define a mean random dynamical system via the solution operators. We then prove the existence and uniqueness of weak pullback mean random attractors. We finally establish the existence of invariant measures of the equations when the diffusion terms are Lipschitz continuous functions.
报告时间：2020年9月4日20:00-22:00
Zoom会议号：984 6166 3714 密码:702229
报告人简介：美国新墨西哥理工学院数学系教授。主要从事确定及随机偏微分方程、无穷维随机动力系统、周期和几乎周期随机系统以及奇异扰动问题等领域的研究。在SIAM Journal on Applied Dynamical Systems，Journal of Differential Equations，Transactions of AMS，Proceedings of Royal Society of Edinburgh等国际期刊发表学术论文80多篇，获美国国家科学基金资助多项。
报告人：段金桥
报告题目：Transition Phenomena in Stochastic Dynamical Systems
摘要: Dynamical systems are often under random fluctuations. The noisy fluctuations may be Gaussian or non-Gaussian, which are modeled by Brownian motion or α-stable Levy motion, respectively. Non-Gaussianity of the noise manifests as nonlocality at a “macroscopic” level. Stochastic dynamical systems with non-Gaussian noise (modeled by α-stable Levy motion) have attracted a lot of attention recently. The non-Gaussianity index α is a significant indicator for various dynamical behaviors.
Transition phenomena are special events of evolution from one metastable state to another in stochastic dynamical systems, caused by the interaction between nonlinearity and uncertainty. Examples for such events are phase transition, pattern change, gene transcription, climate change, abrupt change, extreme transition, and other rare events. The most probable transition pathways are the maximal likely (in the sense of optimizing a probability or an action functional) trajectory between metastable states.
The speaker will present recent work on analyzing and estimating the most probable transition pathways for stochastic dynamical systems, in the context of the Onsager-Machlup action functionals.
报告时间：2020年9月4日10:00
腾讯会议号：272 539 996 密码: 200904
报告人简介：美国伊利诺理工学院（Illinois Institute of Technology）教授。曾任美国国家纯粹与应用数学所副所长（挂靠在美国加州大学洛杉矶分校，Institute for Pure and Applied Mathematics, www.ipam.ucla.edu ）。段金桥教授的研究领域包括非线性动力系统，随机动力系统，随机偏微分方程，以及数学与其它学科的交叉研究。段金桥教授在随机动力系统，随机偏微分方程及其在数据科学，地球系统和生物系统应用研究领域作出了重要贡献。 段金桥曾获得欧洲地球物理学会青年科学家论文奖。他现任Stochastics and Dynamics (“随机动力系统”) 杂志管理编辑。他还任Interdisciplinary Mathematical Sciences (“跨学科应用数学丛书”) 主编，以及“Nonlinear Processes in Geophysics”编委。
