Mathematical Sciences: Global Uniqueness and Stability in Inverse Problems for PDE

本课题将研究已知逆问题解的唯一性和稳定性。这些问题出现在许多不同的领域，如地球物理学、电断层成像、裂缝检测、地震预测以及声学和地震勘探。基本的数学问题将通过使用先进的技术，如卡尔曼估计和卡尔德隆-西尔维斯特-乌尔曼方法来研究。

This project will study uniqueness and stability of solutions of well known inverse problems. This problems arise in areas as diverse as geophysics, electrical tomography, crack detection, earthquake prediction, and acoustic and seismic prospecting. Fundamental mathematical issues will be studied through the use of advanced techniques such as Carleman estimates and Calderon- Sylvester-Uhlmann methods.