[Détermination d'un terme source dans une équation parabolique dégénérée à partir d'une observation interne localisée]
Le but de cette Note est de montrer un résultat d'unicité et stabilité pour un problème inverse consistant à déterminer un terme source dans une équation parabolique dégénérée en dimension 1. On reprend la méthode introduite par Imanuvilov et Yamamoto en 1998 en précisant une inégalité de Carleman récente obtenue par Cannarsa, Martinez et Vancostenoble.
The aim of this Note is to prove a Lipschitz stability and uniqueness result for an inverse source problem relative to a one-dimensional degenerate parabolic equation. We use the method introduced by Imanuvilov and Yamamoto in 1998, with the help of some recent Carleman estimate for degenerate equations obtained by Cannarsa, Martinez and Vancostenoble.
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@article{CRMATH_2010__348_23-24_1287_0,
author = {Tort, Jacques},
title = {Determination of source terms in a degenerate parabolic equation from a locally distributed observation},
journal = {Comptes Rendus. Math\'ematique},
pages = {1287--1291},
publisher = {Elsevier},
volume = {348},
number = {23-24},
year = {2010},
doi = {10.1016/j.crma.2010.10.031},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2010.10.031/}
}
TY - JOUR AU - Tort, Jacques TI - Determination of source terms in a degenerate parabolic equation from a locally distributed observation JO - Comptes Rendus. Mathématique PY - 2010 SP - 1287 EP - 1291 VL - 348 IS - 23-24 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.10.031/ DO - 10.1016/j.crma.2010.10.031 LA - en ID - CRMATH_2010__348_23-24_1287_0 ER -
%0 Journal Article %A Tort, Jacques %T Determination of source terms in a degenerate parabolic equation from a locally distributed observation %J Comptes Rendus. Mathématique %D 2010 %P 1287-1291 %V 348 %N 23-24 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2010.10.031/ %R 10.1016/j.crma.2010.10.031 %G en %F CRMATH_2010__348_23-24_1287_0
Tort, Jacques. Determination of source terms in a degenerate parabolic equation from a locally distributed observation. Comptes Rendus. Mathématique, Tome 348 (2010) no. 23-24, pp. 1287-1291. doi : 10.1016/j.crma.2010.10.031. http://www.numdam.org/articles/10.1016/j.crma.2010.10.031/
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