# American Institute of Mathematical Sciences

doi: 10.3934/mcrf.2020054

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

 Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France

* Corresponding author

Received  January 2020 Revised  October 2020 Published  December 2020

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 measurements are located 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 a given non homogeneous boundary condition.

Citation: Laure Cardoulis, Michel Cristofol, Morgan Morancey. A stability result for the diffusion coefficient of the heat operator defined on an unbounded guide. Mathematical Control & Related Fields, doi: 10.3934/mcrf.2020054
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##### References:
Representation of $\Omega_l$ and $\Omega_L$ in a 3D setting
Lighted lateral boundary from $a$
A neighborhood of the lateral boundary
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