AI 中文总结
本文研究从单次时间观测恢复n维热方程势项的反问题，基于Carleman估计证明唯一性并讨论观测最优性。
AI 中文摘要
我们研究了从单个时间解剖面恢复n维热方程势项的反问题。我们证明，在势项在任意子域内已知的假设下，利用固定时刻的解测量，通过稳定性不等式可以唯一确定该势项。该方法基于Carleman估计。此外，我们讨论了此类观测的最优性。
英文摘要
We examine the inverse problem of recovering the potential term of an n-dimensional heat equation from a single time solution profile. We show that it is possible to uniquely determine this potential term via a stability inequality using solution measurements taken at a fixed time, assuming the potential is known within an arbitrary subdomain. The approach is based on the Carleman estimate. Additionally, we discuss the optimality of this type of observation.
Journal refNonlinear Analysis: Theory, Methods and Applications, 273
