Partial Differential Equations
A Carleman estimate for the two dimensional heat equation with mixed boundary conditions
Comptes Rendus. Mathématique, Volume 351 (2013) no. 3-4, pp. 97-100.

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.

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.

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Published online:
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, Volume 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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