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

ESAIM: Control, Optimisation and Calculus of Variations (2002)

- Volume: 7, page 1-22
- ISSN: 1292-8119

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topCanuto, Bruno. "Unique localization of unknown boundaries in a conducting medium from boundary measurements." ESAIM: Control, Optimisation and Calculus of Variations 7 (2002): 1-22. <http://eudml.org/doc/245843>.

@article{Canuto2002,

abstract = {We consider the problem of localizing an inaccessible piece $I$ of the boundary of a conducting medium $\Omega $, and a cavity $D$ contained in $\Omega $, from boundary measurements on the accessible part $A$ of $\partial \Omega $. Assuming that $g(t,\sigma )$ is the given thermal flux for $\left( t,\sigma \right) \in (0,T)\times A$, and that the corresponding output datum is the temperature $u(T_0,\sigma )$ measured at a given time $T_0$ for $\sigma \in A_\{\{\rm out\}\}\subset A$, we prove that $I$ and $D$ are uniquely localized from knowledge of all possible pairs of input-output data $(g,u(T_0)_\{\mid A_\{\{\rm out\}\}\})$. The same result holds when a mean value of the temperature is measured over a small interval of time.},

author = {Canuto, Bruno},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {inverse boundary value problems; cavities; corrosion; uniqueness},

language = {eng},

pages = {1-22},

publisher = {EDP-Sciences},

title = {Unique localization of unknown boundaries in a conducting medium from boundary measurements},

url = {http://eudml.org/doc/245843},

volume = {7},

year = {2002},

}

TY - JOUR

AU - Canuto, Bruno

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

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2002

PB - EDP-Sciences

VL - 7

SP - 1

EP - 22

AB - We consider the problem of localizing an inaccessible piece $I$ of the boundary of a conducting medium $\Omega $, and a cavity $D$ contained in $\Omega $, from boundary measurements on the accessible part $A$ of $\partial \Omega $. Assuming that $g(t,\sigma )$ is the given thermal flux for $\left( t,\sigma \right) \in (0,T)\times A$, and that the corresponding output datum is the temperature $u(T_0,\sigma )$ measured at a given time $T_0$ for $\sigma \in A_{{\rm out}}\subset A$, we prove that $I$ and $D$ are uniquely localized from knowledge of all possible pairs of input-output data $(g,u(T_0)_{\mid A_{{\rm out}}})$. The same result holds when a mean value of the temperature is measured over a small interval of time.

LA - eng

KW - inverse boundary value problems; cavities; corrosion; uniqueness

UR - http://eudml.org/doc/245843

ER -

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