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.

许多物理和生物科学的基础模型的分析都受到奇点的阻碍。本项目旨在发现和分类两类重要的非线性方程的奇异解：椭圆型和抛物型。该项目希望通过使用几何分析和动力系统的创新方法来产生新的方法来破译奇点。该项目的预期成果包括新的和强大的工具，以推进更一般的奇点理论。这将带来巨大的好处，例如在国际研究前沿的奇点关键问题上获得新的数学知识，并增强澳大利亚在全球公认领域的专业知识。