Geometric Analysis

几何分析

• 批准号: 1000226205-2011
• 负责人: Guan, Pengfei
• 金额: $ 14.57万
• 依托单位: McGill University
• 依托单位国家: 加拿大
• 项目类别: Canada Research Chairs
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=652575
• 关键词: Geometric; Analysis

Nonlinear partial differential equations arise naturally in the study of physical*phenomena . We propose to study some of these equations related to problems in geometry. These lead to challenging questions in nonlinear differential equations which points to the direction of geometric analysis. Our objective is to develop various analytic tools for these equations, investigate structures of geometric solutions, qualitative properties of solutions, and derive geometric and topological consequences. Advances in the theory of these equations will lead to the solutions of the proposed problems in geometry, will enrich the existing theory of fully nonlinear partial differential equations in general, with applications in heat type flows and nonlinear equations in plasma and material science.

非线性偏微分方程自然出现在物理*现象的研究中。我们建议研究与几何问题有关的一些方程。这些导致非线性微分方程中有具有挑战性的问题，该方程指向几何分析的方向。我们的目标是为这些方程开发各种分析工具，研究几何解决方案的结构，解决方案的定性特性，并得出几何和拓扑后果。这些方程式理论的进步将导致几何形状中提出问题的解决方案，一般来说，将在热量流中的应用中充实现有的完全非线性部分偏微分方程的理论，以及在血浆和材料科学中的非线性方程。