Mathematical Sciences: Research in Nonlinear Problems Arising in Mechanics

数学科学：力学中非线性问题的研究

• 批准号: 9406295
• 负责人: Marshall Slemrod
• 金额: $ 5万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-06-15 至 1996-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9406295&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Nonlinear; Problems

9406295 Slemrod This proposal outlines proposed research in three areas: (i) kinetic modeling of gases exhibiting change of phase and metastable states, (ii) resolution of Riemann problems of hyperbolic systems of conservation laws via hydrodynamic and viscous limits, (iii) analysis of the structure of shock waves for spherically symmetric three dimensional fluid flow. The main goal is the understanding of the dynamics of these highly nonlinear phenomena and applying this insight to interpretation of the motivating physical problems. The technical approach to the above research will be to (i) examine cluster Boltzmann like dynamics and try to simulate van de Waals intermolecular attractions to develop discrete velocity phase transition models: (ii) apply self similar scaling methods to recover hydrodynamic and viscous limits for systems of conservation laws, (iii) impliment the viscous self similarity method to the analysis of spherically symmetric gas dynamics (conservation laws of mass, momentum, energy).

小行星9406295 该建议概述了三个领域的拟议研究：（一）动力学模拟的气体表现出相变和亚稳态，（二）通过流体动力学和粘性限制的双曲守恒律系统的黎曼问题的决议，（三）分析的结构的冲击波的球对称三维流体流动。主要目标是理解这些高度非线性现象的动力学，并将这种见解应用于解释激励物理问题。 上述研究的技术方法将是（i）检查团簇玻尔兹曼动力学，并尝试模拟货车德瓦尔斯分子间吸引力，以开发离散速度相变模型：（ii）应用自相似标度方法来恢复守恒律系统的流体动力学和粘性极限，（3）将粘性自相似方法应用于球对称气体动力学（质量、动量、能量守恒定律）的分析。