Null controllability for parabolic equations with dynamic boundary conditions

Lahcen Maniar; Martin Meyries; Roland Schnaubelt

doi:10.3934/eect.2017020

Article Contents

2017, Volume 6, Issue 3: 381-407. Doi: 10.3934/eect.2017020

This issue Previous Article Local exact controllability to trajectories of the magneto-micropolar fluid equations Next Article $\mathbb{L}^p-$solutions of the stochastic Navier-Stokes equations subject to Lévy noise with $\mathbb{L}^m(\mathbb{R}^m)$ initial data

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: October 2017

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.

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Abstract

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.

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Mathematics Subject Classification: Primary: 93B05; Secondary: 35K20, 93B07.

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References

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