Electron. J. Diff. Equ., Vol. 2014 (2014), No. 167, pp. 1-26.

Lipschitz stability for linear parabolic systems with interior degeneracy

Idriss Boutaayamou, Genni Fragnelli, Lahcen Maniar

Abstract:
In this article, we study an inverse problem for linear degenerate parabolic systems with one force. We establish Lipschitz stability for the source term from measurements of one component of the solution at a positive time and on a subset of the space domain, which contains degeneracy points. The key ingredient is the derivation of a Carleman-type estimate.

Submitted June 28, 2014. Published July 30, 2014.
Math Subject Classifications: 35k65.
Key Words: Parabolic system; interior degeneracy; Carleman estimates; Lipschitz stability.

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Idriss Boutaayamou
Département de Mathématiques
Faculté des Sciences Semlalia, LMDP, UMMISCO (IRD-UPMC)
Université Cadi Ayyad, Marrakech 40000, B.P. 2390, Morocco
email: dsboutaayamou@gmail.com
Genni Fragnelli
Dipartimento di Matematica
Universitá degli Studi di Bari Aldo Moro
Via E. Orabona 4, 70125 Bari - Italy
email: genni.fragnelli@uniba.it
Lahcen Maniar
Département de Mathématiques
Faculté des Sciences Semlalia, LMDP, UMMISCO (IRD-UPMC)
Université Cadi Ayyad, Marrakech 40000, B.P. 2390, Morocco
email: maniar@uca.ma

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