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Journal Articles Mathematical Control and Related Fields Year : 2021

A stability result for the diffusion coefficient of the heat operator defined on an unbounded guide

Laure Cardoulis
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Michel Cristofol
Morgan Morancey

Abstract

In this article we consider the inverse problem of determining the diffusion coefficient of the heat operator in an unbounded guide using a finite number of localized observations. For this problem, we prove a stability estimate in any finite portion of the guide using an adapted Carleman inequality. The boundary measurements are also realized on the boundary of a larger finite portion of the guide. A special care is required to avoid measurements on the cross-section boundaries which are inside the actual guide. This stability estimate uses a technical positivity assumption. Using arguments from control theory, we manage to remove this assumption for the inverse problem with non homogeneous given boundary conditions.
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Dates and versions

hal-02467778 , version 1 (05-02-2020)
hal-02467778 , version 2 (08-02-2022)

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Laure Cardoulis, Michel Cristofol, Morgan Morancey. A stability result for the diffusion coefficient of the heat operator defined on an unbounded guide. Mathematical Control and Related Fields, 2021, 11 (4), ⟨10.3934/mcrf.2020054⟩. ⟨hal-02467778v2⟩
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