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arXiv · 2009.09710

Inverse parabolic problems of determining functions with one spatial-component independence by Carleman estimate

Oleg Yu. Imanuvilov·Yavar Kian·Masahiro Yamamoto
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Abstract

For an initial-boundary value problem for a parabolic equation in the spatial variable $x=(x_1,.., x_n)$ and time $t$, we consider an inverse problem of determining a coefficient which is independent of one spatial component $x_n$ by extra lateral boundary data. We apply a Carleman estimate to prove a conditional stability estimate for the inverse problem. Also we prove similar results for the corresponding inverse source problem.

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Oleg Yu. Imanuvilov, Yavar Kian, Masahiro Yamamoto. 2020-09-21. Inverse parabolic problems of determining functions with one spatial-component independence by Carleman estimate. https://arxiv.org/abs/2009.09710

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