Singular solutions for nonlinear elliptic and parabolic equations

非线性椭圆方程和抛物方程的奇异解

• 批准号: DP220101816
• 负责人: Prof Florica Cirstea
• 金额: $ 30.44万
• 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: 2022
• 资助国家: 澳大利亚
• 起止时间: 2022-04-12 至 2025-04-11
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP220101816
• 关键词: Singular; solutions; nonlinear; elliptic; parabolic

The analysis of many models fundamental to physical and biological sciences is obstructed by singularities. This project aims to discover and classify the singular solutions for two important types of nonlinear equations: elliptic and parabolic. The project expects to generate novel methods to decipher singularities by using innovative approaches from geometric analysis and dynamical systems. Expected outcomes of this project include new and powerful tools to advance a more general theory of singularities. This should provide significant benefits, such as new mathematical knowledge on key issues on singularities lying at the forefront of international research and enhanced expertise in an area of worldwide recognition for Australia.

奇点阻碍了许多物理和生物科学基础的模型的分析。该项目旨在发现和分类两种重要类型的非线性方程式的奇异解决方案：椭圆形和抛物线。该项目希望通过使用几何分析和动力学系统的创新方法来生成新颖的方法来破译奇异性。该项目的预期结果包括新的和强大的工具，以推进更一般的奇异性理论。这将提供重大的好处，例如有关在国际研究最前沿的关键问题的新​​数学知识，并在全球范围内对澳大利亚认可方面的专业知识增强了专业知识。