Stability Estimates for Some Parabolic Inverse Problems With the Final Overdetermination via a New Carleman Estimate
Mathematical Physics
2024-01-17 v4 math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.2301.09735,
title = {Stability Estimates for Some Parabolic Inverse Problems With the Final Overdetermination via a New Carleman Estimate},
author = {Michael V. Klibanov},
journal= {arXiv preprint arXiv:2301.09735},
year = {2024}
}