Nonlinear Partial Differential Equations

非线性偏微分方程

• 批准号: CRC-2019-00415
• 负责人: Wei, Juncheng
• 金额: $ 14.57万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Canada Research Chairs
• 财政年份: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=730826
• 关键词: Nonlinear; Partial; Differential; Equations

Tornadoes and hurricanes are two examples of singularities in nature. Like all atmospheric phenomena, they must comply with the laws of Physics, expressed in mathematical form by Partial Differential Equations. Mathematically, solutions to PDE's that display abrupt changes in level (``interfaces''), or tornado-like rotation (``vortices'') are called singularities, and the challenge of understanding the mechanisms of singularity formation is a hot current topic. A rich collection of innovative methods is required. Recently we have developed and applied ``gluing methods''to produce striking examples and answer long-open questions. In the years ahead, I propose to build a unified framework for these methods and use it to study singularity formation in a diverse range of problems arising from geometry, physics, biology, chemistry, and social interactions.

龙卷风和飓风是自然界中奇异性的两个例子。像所有大气现象一样，它们必须遵守物理定律，以数学形式通过部分微分方程表示。从数学上讲，PDE的解决方案显示出级别的突然变化（``接口''）或类似龙卷风的旋转（````vortices''）被称为奇异性，并且了解奇异性形成机制的挑战是热门主题。需要丰富的创新方法。 Recently we have developed and applied ``gluing methods''to produce striking examples and answer long-open questions.在未来的几年中，我建议为这些方法建立一个统一的框架，并使用它来研究由几何，物理，生物学，化学和社交互动引起的各种问题的奇异性形成。