Mathematical Sciences: An Inverse Spectral Theory Problem for Bounded Domains in Two or More Dimensions

数学科学：二维或多维有界域的反谱理论问题

• 批准号: 8713722
• 负责人: Joyce McLaughlin
• 金额: $ 3.4万
• 依托单位: Rensselaer Polytechnic Institute
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-11-01 至 1990-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8713722&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Inverse; Spectral; Theory

Given a linear differential equation which may model a physical system one may seek the solutions based on a knowledge of the coefficients. The problem being addresses here is the inverse problem: Given some knowledge of the solutions try to determine the particular differential equation and hence the underlying physical system. The proposed research is directed to handle inverse problems in dimensions two or more based on the success achieved by the investigator with one-dimensional problems.

给定一个可以模拟物理系统的线性微分方程，人们可以基于系数的知识来寻求解。 这里要解决的问题是反问题：在给出一些解的知识的情况下，尝试确定特定的微分方程，从而确定底层的物理系统。 所提出的研究旨在基于研究者在一维问题上所取得的成功来处理二维或更多维度的逆问题。