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September  2017, 6(3): 381-407. doi: 10.3934/eect.2017020

## Null controllability for parabolic equations with dynamic boundary conditions

 1 Cadi Ayyad University, LMDP, UMMISCO (IRD-UPMC) B.P. 2390, Marrakesh, Morocco 2 Institut für Mathematik, Martin-Luther-Universität Halle-Wittenberg, 06099 Halle, Germany 3 Department of Mathematics, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany

Received  August 2015 Revised  March 2017 Published  July 2017

Fund Project: We thank the Deutsche Forschungsgemeinschaft which supported this research within the grants ME 3848/1-1 and SCHN 570/4-1. M.M. thanks L.M. for a very pleasant stay in Marrakesh, where parts of this work originated.

We prove null controllability for linear and semilinear heat equations with dynamic boundary conditions of surface diffusion type. The results are based on a new Carleman estimate for this type of boundary conditions.

Citation: Lahcen Maniar, Martin Meyries, Roland Schnaubelt. Null controllability for parabolic equations with dynamic boundary conditions. Evolution Equations & Control Theory, 2017, 6 (3) : 381-407. doi: 10.3934/eect.2017020
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##### References:
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