报告题目: Convergence Rates of Tikhonov Regularizations for Elliptic and Parabolic Inverse Radiativity Problems
报告人：蒋代军（华中师范大学）
邀请人：郑光辉
报告时间： 2023年6月10日(周六上午) 10:00-11:00
报告地点: 数学院 425
报告摘要: In this talk, we shall study the convergence rates of the Tikhonov regularized solutions for the recovery of the radiativities in elliptic and parabolic systems in general dimensional spaces. The conditional stability estimates are first derived. Due to the difficulty of the verification of the existing source conditions or nonlinearity conditions of the inverse radiativity problems in high dimensional spaces, some new variational source conditions are proposed. The conditions are rigorously verified in general dimensional spaces under the conditional stability estimates. We will also derive the reasonable convergence rates under the new source conditions, and the results reveal the explicit relation between the regularity of the radiativities and the convergence rates.
报告人简介: 蒋代军，华中师范大学副教授，2007年获得华中师范大学学士学位，2009年和2012年分别获得武汉大学硕士和博士学位。蒋代军博士的研究领域包括偏微分方程反问题、稀疏优化及控制，快速算法等，主持国家自然科学基金项目4项，在SIAM系列, Inverse Problems等刊物上发表论文近30篇。
