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

Canuto, 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 -