Stochastic partial differential equations with singular noise (B02)

具有奇异噪声的随机偏微分方程（B02）

• 批准号: 366802323
• 金额: --
• 依托单位: Chinese Academy of Sciences (CAS)
• 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 2020-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/366802323?language=en
• 关键词: Stochastic; partial; differential; equations; singular

This project consists of two parts:(I) Strong approach to stochastic partial differential equations with singular noise: We plan to study global well-posedness, properties and approximations of stochastic partial differential equations with singular noise, based on the theory of regularity structures proposed by Hairer and on the paracontrolled distributions method introduced by Gubinelli, Imkeller and Perkowski.(II) Weak approach to stochastic partial differential equations with singular noise: The aim here is to construct and analyze weak solutions to singular stochastic partial differential equations by using both Dirichlet form theory and the energy solution method recently introduced by Gonçalves and Jara.

（1）奇异噪声随机偏微分方程的强逼近：我们计划基于Hairer提出的正则结构理论和Gubinelli，Imkeller和Perkowski提出的仿控制分布方法，研究奇异噪声随机偏微分方程的整体适定性、性质和逼近。(II)带奇异噪声的随机偏微分方程的弱方法：本文的目的是利用Dirichlet形式理论和Gonçalves和Jara最近提出的能量解方法构造和分析奇异随机偏微分方程的弱解。