# Unique Localization of Unknown Boundaries in a Conducting Medium from Boundary Measurements

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- 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 (2010): 1-22. <http://eudml.org/doc/90591>.

@article{Canuto2010,

abstract = {
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 ∂Ω. Assuming that g(t,σ) is
the given thermal flux for (t,σ) ∈ (0,T) x A, and
that the corresponding output datum is the temperature u(T0,σ)
measured at a given time T0 for σ ∈ Aout ⊂ 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.; inverse boundary value problems; corrosion; uniqueness},

language = {eng},

month = {3},

pages = {1-22},

publisher = {EDP Sciences},

title = {Unique Localization of Unknown Boundaries in a Conducting Medium from Boundary Measurements},

url = {http://eudml.org/doc/90591},

volume = {7},

year = {2010},

}

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

DA - 2010/3//

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 Ω, and
a cavity D contained in Ω, from boundary measurements on the
accessible part A of ∂Ω. Assuming that g(t,σ) is
the given thermal flux for (t,σ) ∈ (0,T) x A, and
that the corresponding output datum is the temperature u(T0,σ)
measured at a given time T0 for σ ∈ Aout ⊂ 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.; inverse boundary value problems; corrosion; uniqueness

UR - http://eudml.org/doc/90591

ER -

## References

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- S. Vessella, Private Comunication.

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