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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
主要研究人员将继续研究非线性波理论的三个主要领域:非线性色散波、弱激波在焦散线处的聚焦和方波爆轰中的灾难性不稳定性。研究方法包括使用解析和渐近技术,辅之以数值分析。之所以需要这样一种综合方法,是因为所研究的现象发生在现有理论的边界上。自然界中的许多现象不能用线性模型来充分描述;自然界天生就是“非线性的”。建议的研究涉及由非线性微分方程组描述的波动的研究。一个很好的例子是,当海浪接近海滩时,海浪“破裂”。为了描述这种非线性波的行为,首席研究人员将结合数值分析使用渐近分析,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