Nonlinear partial differential equations with anisotropy and singularities

具有各向异性和奇点的非线性偏微分方程

• 批准号: DP190102948
• 负责人: Prof Florica Cirstea
• 金额: $ 29.44万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2019
• 资助国家: 澳大利亚
• 起止时间: 2019-01-01 至 2024-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP190102948
• 关键词: Nonlinear; partial; differential; equations; anisotropy

This project aims to develop new methods in the study of several classes of nonlinear partial differential equations featuring singularities and nonstandard growth conditions. The understanding of countless phenomena in physical and biological sciences is impaired by singularities arising naturally in the models of nonlinear partial differential equations. In a systematic study of singularities on important problems, this project aims to advance new analytical methods and settle fundamental questions that remain open. Outcomes include a more inclusive singularity theory, which fully describes all the singularities that can occur. More immediate applications are in core areas of mathematics, which bear significance to quantum mechanics and image processing in particular.

本计画旨在发展新的方法来研究几类具奇异性与非标准增长条件的非线性偏微分方程。物理和生物科学中无数现象的理解受到非线性偏微分方程模型中自然产生的奇点的影响。在系统研究奇点的重要问题，该项目旨在推进新的分析方法和解决仍然开放的基本问题。结果包括一个更具包容性的奇点理论，它充分描述了所有可能发生的奇点。更直接的应用是在数学的核心领域，特别是对量子力学和图像处理具有重要意义。