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 |
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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. |
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ISSN: | 0167-8019 1572-9036 |
DOI: | 10.1007/s10440-014-9871-6 |