Nonlinear Partial Differential Equations, Concentration Phenomena, and Applications

非线性偏微分方程、浓度现象及应用

• 批准号: 1000228597-2012
• 负责人: Wei, Juncheng
• 金额: $ 7.29万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Canada Research Chairs
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=695624
• 关键词: Nonlinear; Partial; Differential; Equations; Concentration

The proposal focuses on theoretical and interdisciplinary studies of concentration phenomena in Nonlinear Partial Differential Equations (NPDEs). Driven by reaction, diffusion and geometry, concentration phenomena appear as one of the central features in various phenomena in differential geometry (bubbling in Yamabe problem), mathematical biology (Spots and Stripes), chemistry and physics, These topics are one of the most important and active areas in the field of NPDEs. On the theoretical side, we expect to make substantial progress on fundamental problems such as classifying entire solutions and geometrization program of elliptic equations, and maintain our edge in key areas; on the applied side, our investigations will explore new frontiers in mathematical biology, material science, image processing and social sciences. We aim to excel in some of key research areas in pure and applied mathematics, in particular to become a leading centre for applied analysis and NPDEs internationally.

该提案侧重于非线性偏微分方程（NPDE）中浓度现象的理论和跨学科研究。 在反应、扩散和几何的驱动下，浓度现象是微分几何（Yamabe问题中的冒泡）、数学生物学（Spots and Stripes）、化学和物理学中各种现象的中心特征之一，是非偏微分方程领域中最重要和最活跃的研究课题之一。 在理论方面，我们期望在基础问题上取得实质性进展，如椭圆方程的整体解分类和几何化程序，并保持我们在关键领域的优势;在应用方面，我们的研究将探索数学生物学，材料科学，图像处理和社会科学的新前沿。 我们的目标是在纯数学和应用数学的一些关键研究领域中脱颖而出，特别是成为国际上应用分析和NPDE的领先中心。