no. 3-4
Partial Differential Equations
A Carleman estimate for the two dimensional heat equation with mixed boundary conditions
[Inégalité de Carleman pour lʼéquation de la chaleur avec conditions mixtes en dimension deux]

Présenté par : Gilles Lebeau

Ali Ziane, Tarik1 ; Ouzzane, Hadjer1 ; Zair, Ouahiba1
1 USTHB, laboratoire AMNEDP, faculté de mathématiques, B.P. 32, El Alia, Bab Ezzouar, 16111 Alger, Algeria
Comptes Rendus. Mathématique, Tome 351 (2013) no. 3-4, pp. 97-100.

Il est bien connu que dans un ouvert régulier, les solutions du problème mêlé pour lʼéquation de Laplace présentent des singularités. Le but de ce travail est dʼétablir une inégalité de Carleman pour lʼéquation de la chaleur en dimension deux en présence de ces singularités.

It is well known that in a regular domain, the solutions of the Laplace equation with mixed boundary conditions can present a singular part. In this work, we prove a Carleman estimate for the two dimensional domain heat equation in presence of these singularities.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.02.006
Ali Ziane, Tarik 1 ; Ouzzane, Hadjer 1 ; Zair, Ouahiba 1

1 USTHB, laboratoire AMNEDP, faculté de mathématiques, B.P. 32, El Alia, Bab Ezzouar, 16111 Alger, Algeria 
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Ali Ziane, Tarik; Ouzzane, Hadjer; Zair, Ouahiba. A Carleman estimate for the two dimensional heat equation with mixed boundary conditions. Comptes Rendus. Mathématique, Tome 351 (2013) no. 3-4, pp. 97-100. doi : 10.1016/j.crma.2013.02.006. http://www.numdam.org/articles/10.1016/j.crma.2013.02.006/

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