Geometric evolution problems in nonlinear partial differential equations

非线性偏微分方程中的几何演化问题

• 批准号: DP150101275
• 负责人: A/Prof Min-Chun Hong
• 金额: $ 22.46万
• 依托单位: The University of Queensland
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2015
• 资助国家: 澳大利亚
• 起止时间: 2015-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP150101275
• 关键词: Geometric; evolution; problems; nonlinear; partial

This project aims to address important problems key to the understanding of geometric evolution equations and certain other nonlinear partial differential equations. The problems to be tackled lie in a very active area of mathematics: harmonic maps, liquid crystals and Yang-Mills theory. Special aims are to exploit new methods to settle open problems in harmonic maps and Yang-Mills equations, and to improve understanding of practical questions such as the mathematical modelling of liquid crystals via the celebrated Ericksen-Leslie and Landau-de Gennes theories. The expected outcomes are fundamental results in mathematics, with applications in other sciences.

这个项目的目的是解决重要问题的关键理解几何发展方程和某些其他非线性偏微分方程。要解决的问题在于一个非常活跃的数学领域：调和映射，液晶和杨米尔斯理论。特别的目的是探索新的方法来解决调和映射和杨米尔斯方程中的开放问题，并通过著名的埃里克森-莱斯利和朗道-德热内理论来提高对实际问题的理解，如液晶的数学建模。预期成果是数学的基本成果，并在其他科学中应用。