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Mathematical Sciences: Floquet Theory for Periodic PDE

Mathematical Sciences: Floquet Theory for Periodic PDE
数学科学:周期偏微分方程的 Floquet 理论
批准号:
9102111
负责人:
Peter Kuchment
金额:
$4.08万
依托单位:
依托单位国家:
美国
项目类别:
Standard Grant
财政年份:
1991
资助国家:
美国
项目状态:
已结题
起止时间:
1991-06-01 至 1993-11-30

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中文摘要
翻译
本课题将研究具有周期系数的椭圆型和抛物型方程的Floquet指数、Floquet展开式以及解的相关性质。重点将放在了解弗洛奎指数集的几何、解在弗洛奎解方面的展开、以及弗洛奎指数的几何与给定方程的性质之间的联系。这些研究的动机是数学物理领域中出现的问题,如稳定性理论、固体量子理论、流体动力学和逆散射理论。
英文摘要
This project will investigate Floquet exponents, Floquet expansions, and related properties of solutions to elliptic and parabolic equations with periodic coefficients. Emphasis will be placed on the understanding of the geometry of the set of Floquet exponents, expansion of solutions in terms of Floquet solutions, and the connections between the geometry of the Floquet exponents and the properties of the given equation. These studies have been motivated by problems arising in areas of mathematical physics such as stability theory, quantum theory of solids, hydrodynamics, and inverse scattering theory.
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Spectral problems of mathematical physics and material science
  • 批准号:
    2007408
  • 项目类别:
    Standard Grant
  • 资助金额:
    $20.14万
  • 财政年份:
    2020
  • 负责人:
    Peter Kuchment
  • 依托单位:
Inverse Problems for Biomedical Imaging and Homeland Security
  • 批准号:
    1816430
  • 项目类别:
    Standard Grant
  • 资助金额:
    $21.37万
  • 财政年份:
    2018
  • 负责人:
    Peter Kuchment
  • 依托单位:
Spectral Problems of Mathematical Physics Related to Novel Materials Science and Photonics
  • 批准号:
    1517938
  • 项目类别:
    Standard Grant
  • 资助金额:
    $22.45万
  • 财政年份:
    2015
  • 负责人:
    Peter Kuchment
  • 依托单位:
Collaborative research: Mathematics of emerging imaging methods in medicine and homeland security
  • 批准号:
    1211463
  • 项目类别:
    Continuing Grant
  • 资助金额:
    $41.58万
  • 财政年份:
    2012
  • 负责人:
    Peter Kuchment
  • 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