Unique localization of unknown boundaries in a conducting medium from boundary measurements

Canuto, Bruno

doi:10.1051/cocv:2002001

Canuto, Bruno

ESAIM: Control, Optimisation and Calculus of Variations, Tome 7 (2002), pp. 1-22.

Résumé

We consider the problem of localizing an inaccessible piece $I$ of the boundary of a conducting medium $Ω$ , and a cavity $D$ contained in $Ω$ , from boundary measurements on the accessible part $A$ of $\partial Ω$ . Assuming that $g (t, σ)$ is the given thermal flux for $(t, σ) \in (0, T) \times A$ , and that the corresponding output datum is the temperature $u (T_{0}, σ)$ measured at a given time $T_{0}$ for $σ \in A_{out} \subset A$ , we prove that $I$ and $D$ are uniquely localized from knowledge of all possible pairs of input-output data $(g, u {(T_{0})}_{∣ A_{out}})$ . The same result holds when a mean value of the temperature is measured over a small interval of time.

MR Zbl

DOI : 10.1051/cocv:2002001

Classification : 35R30
Mots-clés : inverse boundary value problems, cavities, corrosion, uniqueness

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     author = {Canuto, Bruno},
     title = {Unique localization of unknown boundaries in a conducting medium from boundary measurements},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1--22},
     publisher = {EDP-Sciences},
     volume = {7},
     year = {2002},
     doi = {10.1051/cocv:2002001},
     mrnumber = {1925019},
     zbl = {1053.35128},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/cocv:2002001/}
}

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Canuto, Bruno. Unique localization of unknown boundaries in a conducting medium from boundary measurements. ESAIM: Control, Optimisation and Calculus of Variations, Tome 7 (2002), pp. 1-22. doi : 10.1051/cocv:2002001. http://archive.numdam.org/articles/10.1051/cocv:2002001/

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