Null Controllability of Three-dimensional Heat Equation in Singular Domains

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....

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Veröffentlicht in:Acta applicandae mathematicae 2014-12, Vol.134 (1), p.87-109
1. Verfasser: Belghazi, A. H.
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0167-8019
1572-9036
DOI:10.1007/s10440-014-9871-6