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Mathematical Sciences: Waves in Nonlinear Dispersive and Hyperbolic Systems

Mathematical Sciences: Waves in Nonlinear Dispersive and Hyperbolic Systems
数学科学:非线性色散和双曲系统中的波
批准号:
9008520
负责人:
Rodolfo Rosales
金额:
$19.5万
依托单位国家:
美国
项目类别:
Continuing Grant
财政年份:
1990
资助国家:
美国
项目状态:
已结题
起止时间:
1990-06-15 至 1993-11-30

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中文摘要
翻译
首席研究员将继续他的重要研究, 非线性波动理论的三个主要领域:非线性色散 弱冲击波聚焦焦散线和灾难性 方波爆炸的不稳定性 学习方法 涉及分析和渐近技术的使用 并辅以数值分析。 这样一种综合办法 之所以需要,是因为所研究的现象发生在 现有理论的边界。 自然界中的许多现象 用线性模型充分描述;自然是固有的 “非线性”。 拟议的研究涉及波的研究 由非线性微分方程描述的运动。 一个很好的例子是“打破”的海浪,因为它 接近海滩。 为了描述这种行为, 一个非线性波,首席研究员将使用渐近 分析与数值分析相结合,以获得定性 和定量信息。
英文摘要
The principal investigator will continue his important studies of three major areas of nonlinear wave theory: nonlinear dispersive waves, focussing of weak shock waves at caustics and catastrophic instabilities in square-wave detonations. The methods of study involve the use of analytic and asymptotic techniques supplemented with numerical analysis. Such a combined approach is called for because the phenomena under study occur at the boundaries of existing theories. Many phenomena in nature cannot be described adequately with linear models; nature is inherently "nonlinear". The proposed research involves the study of wave motions that are described by nonlinear differential equations. A good example is the "breaking" of an ocean wave as it approaches the beach. In order to describe the behavior of such a nonlinear wave the principal investigator will use asymptotic analysis in concert with numerical analysis to obtain qualitative and quantitative information.
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会议论文
Collaborative Research: Overcoming Order Reduction and Stability Restrictions in High-Order Time-Stepping
Collaborative Research: Gradient-augmented level set methods and jet schemes
  • 批准号:
    1318942
  • 项目类别:
    Continuing Grant
  • 资助金额:
    $17.68万
  • 财政年份:
    2013
  • 负责人:
    Rodolfo Rosales
  • 依托单位:
Collaborative Research: Numerical approaches for incompressible viscous flows with high order accuracy up to the boundary
Collaborative Research: Phantom traffic jams, continuum modeling, and connections with detonation wave theory
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