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Null Controllability of Three-dimensional Heat Equation in Singular Domains

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Abstract

We study in this paper a class of parabolic equations in singular domains. These equations are defined in a singular cylindrical domain whose cross-section contains one reentrant corner or one straight emerging crack. We assume that the diffusion coefficients are non-smooth in the normal direction. We will show some spectral inequality thanks to Carleman type estimates and the construction of a suitable weight function satisfying some properties. As in Benabdallah et al. (C. R. Acad. Sci. Paris 344(6):357–362, 2007), we deduce the null-controllability of these equations with the help of the Lebeau-Robbiano method.

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Acknowledgements

The author wish to thank the referee for his/her comments, suggestions that improve strongly the quality of this paper. The author wish also to thank A. Benabdallah from LATP of CMI (Marseille) and D.E Teniou from AMNEDP (USTHB, Algiers) for numerous useful discussions on the results of this paper.

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Authors and Affiliations

  1. Faculté de mathématiques, Laboratoire AMNEDP, U.S.T.H.B, Algiers, Algeria

    A. H. Belghazi

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  1. A. H. Belghazi
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Correspondence to A. H. Belghazi.

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The author is partially supported by the program Arcus-CERES, ministère des affaires étrangères et Européennes for 50 % and the PNR : Sciences Fondamentales (ANDRU) No. 25/57 for 50.

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Belghazi, A.H. Null Controllability of Three-dimensional Heat Equation in Singular Domains. Acta Appl Math 134, 87–109 (2014). https://doi.org/10.1007/s10440-014-9871-6

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