Free boundary problems in partial differential equations and related topics

偏微分方程中的自由边界问题及相关主题

• 批准号: DP0344111
• 负责人: Prof Yihong Du
• 金额: $ 11.02万
• 依托单位: The University of New England
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2003
• 资助国家: 澳大利亚
• 起止时间: 2003-10-02 至 2006-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP0344111
• 关键词: Free; boundary; problems; partial; differential

We study problems for nonlinear partial differential equations where there is an unknown (free) boundary in the underlying domain. These problems occur when there is a transition from different states of physical systems and arise in many applications of mathematics, such as in population models and in melting problems, to mention but two. We as well discuss related problems motivated by understanding sharp transitions which also have many applications in applied sciences.

我们研究非线性偏微分方程的问题，其中基础域中存在未知（自由）边界。当物理系统的不同状态发生转变时，这些问题就会出现，并出现在数学的许多应用中，例如人口模型和融化问题，仅举两例。我们还讨论了由理解急剧转变所引发的相关问题，这些问题在应用科学中也有许多应用。