Nonlinear harmonic analysis and dispersive partial differential equations

非线性调和分析和色散偏微分方程

• 批准号: DP200101065
• 负责人: A/Prof Adam Sikora
• 金额: $ 29.49万
• 依托单位: Macquarie University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2020
• 资助国家: 澳大利亚
• 起止时间: 2020-04-08 至 2024-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP200101065
• 关键词: Nonlinear; harmonic; analysis; dispersive; partial

This proposal is devoted to linear and nonlinear harmonic analysis. It aims to unify the most significant attributes of harmonic analysis such as restriction estimates, dispersive properties of differential operators, spectral multipliers, uniform Sobolev estimates and sharp Weyl formula. Such unification will strongly improve tools for mathematical modelling in all areas of technology and science. Notable applications include medical imaging, fluid dynamics and subatomic modelling using quantum interpretation. It will solve several important open problems in spectral analysis of partial differential operators and develop new cutting-edge techniques in harmonic analysis with application to nonlinear partial differential equations.

该提案致力于线性和非线性谐波分析。它旨在统一调和分析最重要的属性，例如限制估计、微分算子的色散特性、谱乘数、均匀 Sobolev 估计和锐外尔公式。这种统一将极大地改进所有技术和科学领域的数学建模工具。值得注意的应用包括医学成像、流体动力学和使用量子解释的亚原子建模。 它将解决偏微分算子谱分析中的几个重要的开放问题，并开发调和分析中应用于非线性偏微分方程的新尖端技术。