Mathematical Sciences: Research in Nonlinear Problems Arising in Mechanics

[406295] Slemrod该提案概述了三个领域的研究计划：(i)表现相和亚稳态变化的气体动力学建模；（ii）通过流体动力学和粘性极限解决守恒定律双曲系统的黎曼问题；（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)检查类玻尔兹曼动力学，并尝试模拟范德华分子间引力，以开发离散速度相变模型；（ii）应用自相似缩放方法来恢复守恒定律系统的流体动力学和粘性极限；（iii）实施粘性自相似方法来分析球对称气体动力学（质量、动量、能量守恒定律）。

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).