"Analysis and applications of nonlinear evolution equations: waves, patterns, and singularities."

“非线性演化方程的分析和应用：波、模式和奇点。”

• 批准号: 251124-2012
• 负责人: Gustafson, Stephen
• 金额: $ 1.82万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=508789
• 关键词: Analysis; applications; nonlinear; evolution; equations

The aim of the proposed research is to understand fundamental mathematical equations -- called Partial Differential Equations -- which describe the behaviour of physical systems, such as ferromagnets, superfluids, superconductors, and lasers. The equations are non-linear, cannot be solved explicitly, and are often difficult to solve even with the help of a computer. So we aim instead to obtain a clear picture of how solutions behave -- to determine their essential qualitative features -- by using various mathematical techniques.

拟议的研究的目的是了解基本的数学方程（称为偏微分方程），该方程描述了物理系统的行为，例如铁磁体，超流体，超导体和激光器。方程是非线性的，无法明确解决，即使在计算机的帮助下，通常也难以解决。因此，我们旨在通过使用各种数学技术来清楚地了解解决方案的行为方式（以确定其基本定性特征）。