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
Access Full Article
top
Abstract
topHow to cite
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
top- K. Bryan and L.F. Caudill, An Inverse Problem in Thermal Imaging. SIAM J. Appl. Math.56 (1996) 715-735.
- B. Canuto and O. Kavian, Determining Coefficients in a Class of Heat Equations via Boundary Measurements. SIAM J. Math. Anal. (to appear).
- R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. 1. Wiley, New York (1953).
- N. Garofalo and F.H. Lin, Monotonicity Properties of Variational Integrals, Ap Weights and Unique Continuation. Indiana Univ. Math. J.35 (1986) 245-268.
- O.A. Ladyzhenskaja, V.A. Solonnikov and N.N. Uralceva, Linear and Quasilinear Equations of Parabolic Type. AMS, Providence, RI, Trans. Math. Monographs 23 (1968).
- Rakesh and W.W. Symes, Uniqueness for an Inverse Problem for the Wave Equation. Comm. Partial Differential Equations13 (1988) 87-96.
- J.-C. Saut and B. Scheurer, Unique Continuation for Some Evolution Equations. J. Differential Equations66 (1987) 118-139.
- S. Vessella, Stability Estimates in an Inverse Problem for a Three-Dimensional Heat Equation. SIAM J. Math. Anal.28 (1997) 1354-1370.
- S. Vessella, Private Comunication.
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.