Communications on Pure and Applied Analysis (CPAA)

Stable determination of a semilinear term in a parabolic equation

Pages: 447 - 462, Volume 5, Issue 3, September 2006      doi:10.3934/cpaa.2006.5.447

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Mourad Choulli - Département de Mathématiques, Université de Metz, Ile du Saulcy, 57045 Metz cedex, France (email)
El Maati Ouhabaz - Laboratoire Bordelais d'Analyse et Géométrie, Université Bordeaux 1, 351, cours de la Libération 33405 Talence cedex, France (email)
Masahiro Yamamoto - Graduate School of Mathematical Sciences University of Tokyo, 3-8-1 Komaba, Tokyo, 153-8914, Japan (email)

Abstract: In [5] the first and third authors establish Hölder type stability estimates for the inverse problem consisting in the determination of a semilinear term of a parabolic equation from a single boundary measurement when the domain is a rectangle. In the present paper we extend the results in [5] for a general smooth domain.

Keywords:  semilinear parabolic equation, Hölder type stability estimate, fundamental solution, gaussian lower bound.
Mathematics Subject Classification:  35R30.

Received: April 2005;      Revised: December 2005;      Published: June 2006.