We prove a logarithmic stability estimate for a parabolic inverse problem concerning the localization of unknown cavities in a thermic conducting medium in , , from a single pair of boundary measurements of temperature and thermal flux.
Mots-clés : parabolic equations, strong unique continuation, stability, inverse problems
@article{COCV_2002__7__521_0,
author = {Canuto, B. and Rosset, Edi and Vessella, S.},
title = {A stability result in the localization of cavities in a thermic conducting medium},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {521--565},
publisher = {EDP-Sciences},
volume = {7},
year = {2002},
doi = {10.1051/cocv:2002066},
mrnumber = {1925040},
zbl = {1225.35255},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2002066/}
}
TY - JOUR AU - Canuto, B. AU - Rosset, Edi AU - Vessella, S. TI - A stability result in the localization of cavities in a thermic conducting medium JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2002 SP - 521 EP - 565 VL - 7 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2002066/ DO - 10.1051/cocv:2002066 LA - en ID - COCV_2002__7__521_0 ER -
%0 Journal Article %A Canuto, B. %A Rosset, Edi %A Vessella, S. %T A stability result in the localization of cavities in a thermic conducting medium %J ESAIM: Control, Optimisation and Calculus of Variations %D 2002 %P 521-565 %V 7 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2002066/ %R 10.1051/cocv:2002066 %G en %F COCV_2002__7__521_0
Canuto, B.; Rosset, Edi; Vessella, S. A stability result in the localization of cavities in a thermic conducting medium. ESAIM: Control, Optimisation and Calculus of Variations, Tome 7 (2002), pp. 521-565. doi : 10.1051/cocv:2002066. http://www.numdam.org/articles/10.1051/cocv:2002066/
[1] and, domains and unique continuation at the boundary. Comm. Pure Appl. Math. L (1997) 935-969. | MR | Zbl
[2] and, The inverse conductivity problem with one measurement: Bounds on the size of the unknown object. SIAM J. Appl. Math. 58 (1998) 1060-1071. | MR | Zbl
[3] and, Optimal stability for the inverse problem of multiple cavities. J. Differential Equations 176 (2001) 356-386. | MR | Zbl
[4] ,, and, Optimal stability for inverse elliptic boundary value problems with unknown boundaries. Ann. Scuola Norm. Sup. Pisa Cl. Sci (4) XXIX (2000) 755-806. | Numdam | MR | Zbl
[5] and, An inverse problem in thermal imaging. SIAM J. Appl. Math. 56 (1996) 715-735. | MR | Zbl
[6] and, Uniqueness for boundary identification problem in thermal imaging, in Differential Equations and Computational Simulations III, edited by J. Graef, R. Shivaji, B. Soni and J. Zhu.
[7] and, Stability and reconstruction for an inverse problem for the heat equation. Inverse Problems 14 (1998) 1429-1453. | MR | Zbl
[8] , and, Quantitative estimates of unique continuation for parabolic equations and inverse initial-boundary value problems with unknown boundaries. Trans. AMS 354 (2002) 491-535. | MR | Zbl
[9] and, Methods of Mathematical Physics, Vol. 1. Wiley, New York (1953). | Zbl
[10] and, Elliptic partial differential equations of second order. Springer, New York (1983). | MR | Zbl
[11] , Inverse problems for partial differential equations. Springer, New York (1998). | MR | Zbl
[12] and, A unique continuation theorem for solutions of a parabolic differential equation. J. Math. Soc. Japan 10 (1958) 314-321. | MR | Zbl
[13] , and, Linear and quasilinear equations of parabolic type. Amer. Math. Soc., Providende, Math. Monographs 23 (1968). | Zbl
[14] and, Generalized analyticity and some related properties of solutions of elliptic and parabolic equations. Russ. Math. Surveys 29 (1974) 195-212. | MR | Zbl
[15] , A uniqueness theorem for parabolic equations. Comm. Pure Appl. Math. XLIII (1990) 127-136. | MR | Zbl
[16] and, Non-homogeneous boundary value problems and applications II. Springer, New York (1972). | Zbl
[17] , Semigroups of linear operators and applications to partial differential equations. Springer, New York (1983). | MR | Zbl
[18] , Stability estimates in an inverse problem for a three-dimensional heat equation. SIAM J. Math. Anal. 28 (1997) 1354-1370. | MR | Zbl
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