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Journal d'Analyse Mathématique

, Volume 135, Issue 1, pp 1–35 | Cite as

Carleman estimates for parabolic equations with interior degeneracy and Neumann boundary conditions

  • Idriss Boutaayamou
  • Genni Fragnelli
  • Lahcen Maniar
Article

Abstract

We consider a parabolic problem with degeneracy in the interior of the spatial domain and Neumann boundary conditions. In particular, we focus on the well-posedness of the problem and on Carleman estimates for the associated adjoint problem. The novelty of the present paper is that, for the first time, the problem is considered as one with an interior degeneracy and Neumann boundary conditions, so no previous result can be adapted to this situation. As a consequence, new observability inequalities are established.

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Copyright information

© Hebrew University Magnes Press 2018

Authors and Affiliations

  • Idriss Boutaayamou
    • 1
  • Genni Fragnelli
    • 2
  • Lahcen Maniar
    • 3
  1. 1.Département de Mathématiques, Informatiques et Gestion, Faculté Polydisciplinaire de OuarzazateUniversité Ibn ZohrOuarzazateMorocco
  2. 2.Dipartimento di MatematicaUniversità di Bari “Aldo Moro”BariItaly
  3. 3.Département de Mathématiques, Faculté des Sciences Semlalia, LMDP, UMMISCO (IRD-UPMC)Université Cadi AyyadMarrakechMorocco

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