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Régularité des coefficients de propogation de singularités de l’équation de la chaleur dans un domaine polygonal plan
- Publisher
- Springer Journals
- Copyright
- Copyright © 2014 by Springer Science+Business Media Dordrecht
- Subject
- Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Statistical Physics, Dynamical Systems and Complexity; Mechanics
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- DOI
- 10.1007/s10440-014-9871-6
- Publisher site
- See Article on Publisher Site
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.
Journal
Acta Applicandae Mathematicae – Springer Journals
Published: Feb 25, 2014