Geometric harmonic analysis for diffusive heat equations

扩散热方程的几何调和分析

• 批准号: 261100-2007
• 负责人: Xiao, Jie
• 金额: $ 0.87万
• 依托单位: Memorial University of Newfoundland
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2010
• 资助国家: 加拿大
• 起止时间: 2010-01-01 至 2011-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=455797
• 关键词: Geometric; harmonic; analysis; diffusive; heat

The interaction between harmonic analysis and partial differential equations (PDE) has a long history going back to the Dirichlet problem for the Laplace equation. Nowadays, a fruitful ground for the interplay is the study of various aspects of PDE. With special emphasis on the geometric capacity-measure theory approach, this proposed research program will be centered about the boundary between the above two core areas via the Cauchy problem for the linear-nonlinear heat equations. Particular topics to be investigated include:

调和分析和偏微分方程之间的相互作用有着悠久的历史，可以追溯到拉普拉斯方程的狄利克雷问题。如今，一个富有成效的地面的相互作用是研究的各个方面的偏微分方程。特别强调几何容量测量理论方法，本研究计划将通过线性-非线性热方程的柯西问题围绕上述两个核心区域之间的边界进行。将调查的具体专题包括：