Mathematical Sciences: Research in Nonlinear Problems Arising in Mechanics

9406295这项建议概述了拟在三个领域进行的研究：(I)气体相态和亚稳态变化的动力学模拟，(Ii)通过流体动力学和粘性极限解决双曲型守恒律组的Riemann问题，(Iii)球对称三维流体流动的激波结构分析。主要目标是理解这些高度非线性现象的动力学，并应用这种洞察力来解释激发动机的物理问题。上述研究的技术途径将是(I)考察类Boltzmann团簇动力学，并尝试模拟van de Waals分子间引力以建立离散速度相变模型；(Ii)应用自相似标度方法恢复守恒定律系统的流体动力学和粘性极限；(Iii)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。

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).