通过新型Carleman估计对具有最终超定条件的若干抛物型反问题的稳定性估计
Stability Estimates for Some Parabolic Inverse Problems With the Final Overdetermination via a New Carleman Estimate
AI总结：
本文利用新型Carleman估计，针对具有最终时刻超定数据的一般二阶变系数线性抛物型方程，建立了系数反问题与反源问题的Hölder和Lipschitz稳定性估计及唯一性定理。
摘要：
本文研究一般二阶变系数线性抛物型方程的若干系数反问题及相应的反源问题的Hölder与Lipschitz稳定性估计及唯一性定理。反问题的数据在最终时刻{t=T}给出。此外，Dirichlet和Neumann边界条件均在侧边界的一部分或整个侧边界上给出。因此，如果这些边界条件仅在边界的一部分上给出，那么即使目标系数已知，正问题也不是经典的初边值问题。
英文摘要：
This paper is about Holder and Lipschitz stability estimates and uniqueness theorems for some coefficient inverse problems and associated inverse source problems for a general linear parabolic equation of the second order with variable coefficients. The data for the inverse problem are given at the final moment of time {t=T}. In addition, both Dirichlet and Neumann boundary conditions are given either on a part or on the entire lateral boundary. Thus, if these boundary conditions are given only at a part of the boundary, then even if the target coefficient is known, still the forward problem is not a classical initial boundary value problem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
