Inverse Problems For Partial Differential Equations - A Geometric Analysis Perspective

偏微分方程的反问题 - 几何分析的角度

• 批准号: FT130101346
• 负责人: A/Prof Leo Tzou
• 金额: $ 42.75万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: ARC Future Fellowships
• 财政年份: 2014
• 资助国家: 澳大利亚
• 起止时间: 2014-06-30 至 2018-09-03
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/FT130101346
• 关键词: Inverse; Problems; Partial; Differential; Equations

This project will study mathematical models of various medical imaging techniques. These problems are formulated as inverse problems in partial differential equations (PDE) where one wishes to obtain information about a differential equation from data about its solutions. This problem is not well understood in the geometric setting where the PDE is taking place on a manifold and the goal of this research is to advance the field in this direction. This project will introduce novel and innovative ideas from geometry and topology to overcome some of these difficulties. This project will enrich mathematics by providing links between different fields. Furthermore, it will enable the application of imaging techniques in a broader geometric setting to provide more efficient and accurate non-invasive detection techniques.

该项目将研究各种医学成像技术的数学模型。这些问题被公式化为偏微分方程（PDE）中的反问题，其中人们希望从关于其解的数据中获得关于微分方程的信息。这个问题是没有很好地理解在几何设置偏微分方程是发生在一个流形上，这项研究的目标是推进该领域在这个方向。这个项目将从几何学和拓扑学中引入新颖和创新的想法，以克服其中的一些困难。该项目将通过提供不同领域之间的联系来丰富数学。此外，它将使成像技术在更广泛的几何设置中的应用成为可能，以提供更有效和更准确的非侵入性检测技术。