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

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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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Authors and Affiliations

  1. Département de Mathématiques, Informatiques et Gestion, Faculté Polydisciplinaire de Ouarzazate, Université Ibn Zohr, Ouarzazate, B.P: 638, Morocco

    Idriss Boutaayamou

  2. Dipartimento di Matematica, Università di Bari “Aldo Moro”, Via E. Orabona 4, 70125, Bari, Italy

    Genni Fragnelli

  3. Département de Mathématiques, Faculté des Sciences Semlalia, LMDP, UMMISCO (IRD-UPMC), Université Cadi Ayyad, Marrakech, 40000, B.P. 2390, Morocco

    Lahcen Maniar

Authors
  1. Idriss Boutaayamou
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  2. Genni Fragnelli
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  3. Lahcen Maniar
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Correspondence to Genni Fragnelli.

Additional information

The author is a member of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM) and she is partially supported by the reaserch project Comportamento asintotico e controllo di equazioni di evoluzione non lineari of the GNAMPA-INdAM.

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Boutaayamou, I., Fragnelli, G. & Maniar, L. Carleman estimates for parabolic equations with interior degeneracy and Neumann boundary conditions. JAMA 135, 1–35 (2018). https://doi.org/10.1007/s11854-018-0030-2

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  • DOI: https://doi.org/10.1007/s11854-018-0030-2

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