Nonlinear free boundary problems: Propagation and regularity

非线性自由边界问题：传播和规律性

• 批准号: DE170101410
• 负责人: Dr Maolin Zhou
• 金额: $ 23.11万
• 依托单位: The University of New England
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Early Career Researcher Award
• 财政年份: 2017
• 资助国家: 澳大利亚
• 起止时间: 2017-06-01 至 2020-05-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DE170101410
• 关键词: Nonlinear; free; boundary; problems; Propagation

This project aims to understand the propagation profile and regularity of two important classes of free boundary problems. Nonlinear free boundary problems arise from many applied fields, and pose great challenges to the theory of nonlinear partial differential equations, as the underlying domain of the solution to such problems has to be solved together with the solution itself. This research is expected to enhance the existing theory of partial differential equations, and extend its applications to new situations such as flow through porous media and spreading of invasive species.

本计画旨在了解两类重要的自由边界问题的传播轮廓与规律性。非线性自由边值问题广泛存在于许多应用领域，由于其解的定义域必须与解本身一起求解，因此对非线性偏微分方程理论提出了很大的挑战。该研究有望增强现有的偏微分方程理论，并将其应用扩展到新的情况，如通过多孔介质的流动和入侵物种的传播。