Mathematical Sciences: Inversion and Observability of Parabolic Initial Value Problems

数学科学：抛物线初值问题的反演和可观性

• 批准号: 9008144
• 负责人: David Gilliam
• 金额: $ 1.1万
• 依托单位: Texas Tech University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-08-01 至 1992-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9008144&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Inversion; Observability; Parabolic

The inverse problem of determining the initial boundary conditions of a system evolving in space and time from incomplete observations of the system at various points interior to the spatial domain, is of considerable importance in many engineering and scientific applications. This project deals with a selection of theoretical and numerical aspects of these problems for certain classes of parabolic partial differential equations. Determination of surface temperature and heat flux from a finite set of interior temperature measurements stable under noisy data will be investigated. Theoretical and numerical analysis of methods involving eigenfunction expansions of initial data and Whittaker Cardinal expansions of initial boundary data will be studied.

确定初始边界的反问题 一个系统在空间和时间上从不完全演化的条件 系统内部各点的观测结果 空间域，在许多工程中是相当重要 和科学应用。 这个项目涉及一个选择 这些问题的理论和数值方面， 某些抛物型偏微分方程。 从大气中测定地表温度和热通量 有限的内部温度测量值集， 将研究噪声数据。 理论和数值 初始特征函数展开法的分析 数据和初始边界数据的Whittaker基数展开 将被研究。