课题基金 / 基金详情

Mathematical Sciences: Research in Nonlinear Problems Arising in Mechanics

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:
$5.0万
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
项目状态:
已结题
起止时间:
1994-06-15 至 1996-05-31

项目摘要

项目成果

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中文摘要
翻译
[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)。
英文摘要
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).
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Research on Nonlinear Partial Differential Equations of Compressible Fluid Mechanics
  • 批准号:
    0647554
  • 项目类别:
    Standard Grant
  • 资助金额:
    $13.56万
  • 财政年份:
    2007
  • 负责人:
    Marshall Slemrod
  • 依托单位:
FRG: Collaborative Research: Multi-Dimensional Problems for the Euler Equations of Compressible Fluid Flow and Related Problems in Hyperbolic Conservation Laws
  • 批准号:
    0243722
  • 项目类别:
    Standard Grant
  • 资助金额:
    $13.18万
  • 财政年份:
    2003
  • 负责人:
    Marshall Slemrod
  • 依托单位:
L^1 Stability of Hyperbolic Coservation Laws with Geometrical Sources and Kinetic Equations
  • 批准号:
    0203858
  • 项目类别:
    Standard Grant
  • 资助金额:
    $8.2万
  • 财政年份:
    2002
  • 负责人:
    Marshall Slemrod
  • 依托单位:
Research on Plasma Sheaths: An Interdisciplinary Mathematical-Experimental Program
  • 批准号:
    0071463
  • 项目类别:
    Standard Grant
  • 资助金额:
    $6.93万
  • 财政年份:
    2000
  • 负责人:
    Marshall Slemrod
  • 依托单位:
国内基金
海外基金
Handbook of the Mathematics of the Arts and Sciences的中文翻译
  • 批准号:
    12226504
  • 项目类别:
    数学天元基金项目
  • 资助金额:
    20.0万元
  • 批准年份:
    2022
  • 负责人:
    黄朝凌
  • 依托单位:
SCIENCE CHINA: Earth Sciences
Journal of Environmental Sciences
SCIENCE CHINA Information Sciences