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arXiv · 2301.09735

Stability Estimates for Some Parabolic Inverse Problems With the Final Overdetermination via a New Carleman Estimate

Michael V. Klibanov
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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.

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Michael V. Klibanov. 2023-01-23. Stability Estimates for Some Parabolic Inverse Problems With the Final Overdetermination via a New Carleman Estimate. https://arxiv.org/abs/2301.09735

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