Mathematical Sciences: Inversion and Observability of Parabolic Initial Value Problems

从系统内部各点的不完全观测到空间域，确定系统在空间和时间上演化的初始边界条件的反问题，在许多工程和科学应用中具有相当重要的意义。这个项目处理的选择理论和数值方面的这些问题的某些类别的抛物型偏微分方程。从一组有限的在噪声数据下稳定的室内温度测量中确定表面温度和热流密度将被研究。将研究初始数据的特征函数展开和初始边界数据的惠特克基数展开的理论和数值分析方法。

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.