Mathematical Sciences: Stochastic Partial Differential Equations

数学科学：随机偏微分方程

• 批准号: 9021508
• 负责人: Carl Mueller
• 金额: $ 2.23万
• 依托单位: University of Rochester
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-05-01 至 1993-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9021508&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Stochastic; Partial; Differential

The principal investigator will study partial differential equations with random noise terms. Such equations often arise when physical systems are influenced by noise. This work will consider qualitative properties of solutions in the nonlinear case. There are several goals of this project. The first would involve the carrying over of the coupling technique from the field of infinite particle systems to stochastic partial differential equations. Another goal is the development of Ito's formula for the heat equations with a noise term. Also, propagation of singularities would be studied for random hyperbolic equations.

主要研究者将研究具有随机噪声项的部分微分方程。 当物理系统受噪声影响时，通常会出现这种方程。 这项工作将考虑在非线性情况下解决方案的定性特性。 这个项目有几个目标。 第一个将涉及从无限粒子系统领域到随机偏微分方程的耦合技术的携带。 另一个目标是开发具有噪声项的加热方程的ITO公式。 同样，将研究奇异性的传播，以进行随机双曲方程。