Mathematical Sciences: Nonlinear Partial Differential Equations

数学科学：非线性偏微分方程

• 批准号: 8800347
• 负责人: J. Thomas Beale
• 金额: $ 7.16万
• 依托单位: Duke University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-06-01 至 1991-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8800347&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Nonlinear; Partial; Differential

This research will examine several problems in nonlinear partial differential equations. Vortex methods for simulating time-dependent, three-dimensional, incompressible fluid flows will be extended. Model problems of nonlinear evolution, which are linearly ill-posed but still have predictable behavior, will be studied. The existence of exact solutions of the three- dimensional water wave equations representing obliquely interacting solitary waves or cnoidal water waves will be investigated. This research will extend theoretical understanding of partial differential equations and advance methodology for their numerical solution.

本研究将探讨几个问题，在非线性 偏微分方程 涡方法模拟 非定常三维不可压缩流体流动 将被延长。 非线性演化的模型问题， 是线性不适定的，但仍然有可预测的行为，将 被研究。 三个方程的精确解的存在性 三维水波方程斜 相互作用的孤立波或椭圆余弦水波将 研究了 这项研究将扩展对 偏微分方程及其高级方法 数值解