Harmonic analysis and dispersive partial differential equations

调和分析和色散偏微分方程

• 批准号: DP170101060
• 负责人: A/Prof Zihua Guo
• 金额: $ 24.5万
• 依托单位: Monash University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2017
• 资助国家: 澳大利亚
• 起止时间: 2017-01-01 至 2020-11-01
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP170101060
• 关键词: Harmonic; analysis; dispersive; partial; differential

This project aims to develop theoretical results and practical techniques in the study of Partial Differential Equations. Harmonic analysis is used to study these equations; in which a system’s local behaviour is used to analyse global properties, using techniques such as the Fourier transform. The project will investigate central problems in the area, revealing deep connections between analysis and geometry, and apply these to study the solutions’ long-term behaviour to non-linear equations. Expected outcomes include theoretical results and practical techniques to solve non-linear dispersive equations, which arise in quantum and fluid mechanics.

该项目旨在在研究部分微分方程的研究中开发理论结果和实用技术。谐波分析用于研究这些方程。其中使用诸如傅立叶变换等技术来分析系统的本地行为来分析全局属性。该项目将调查该地区的中心问题，揭示分析与几何形状之间的深厚联系，并将其应用于解决方案的长期行为到非线性方程。预期的结果包括理论结果和实用技术，以解决量子和流体力学中出现的非线性分散方程。