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.

该项目旨在了解两个重要的自由边界问题类别的传播概况和规律性。非线性自由边界问题来自许多应用领域，并对非线性偏微分方程的理论构成了巨大的挑战，因为解决这些问题的解决方案的基本域必须与解决方案本身一起解决。预计这项研究将增强偏微分方程的现有理论，并将其应用扩展到新情况，例如流经多孔培养基和侵入性物种的传播。