Large scale modeling of non-linear microscopic dynamics via singular SPDEs (B09)

通过奇异 SPDE 进行非线性微观动力学的大规模建模 (B09)

• 批准号: 325539554
• 金额: --
• 依托单位: Institut für Angewandte Mathematik (IAM)
• 依托单位国家: 德国
• 项目类别: Collaborative Research Centres
• 财政年份: 2017
• 资助国家: 德国
• 起止时间: 2016-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/325539554?language=en
• 关键词: Large; scale; modeling; non; linear

This project's broad goal is to characterize macroscopic fluctuation of stochastic systems via stochastic differential equations. The nonlinear multiscale features of the models reflect themselves in various interlinked themes: renormalization, singular nonlinear interactions, failure of standard functional spaces, and convergence to universal limits. To successfully address the technical challenges they present we are developing new tools and methods at the boundary between probability and analysis: multilinear dispersive estimates for random fields, paradifferential renormalized decompositions, and singular variational problems.

该项目的主要目标是通过随机微分方程来描述随机系统的宏观波动。模型的非线性多尺度特征反映在各种相互关联的主题中：重整化、奇异非线性相互作用、标准函数空间的失效以及收敛到普遍极限。为了成功地解决他们提出的技术挑战，我们正在开发新的工具和方法之间的边界概率和分析：随机场，paradifferentialrenormalized分解和奇异变分问题的多线性色散估计。