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arXiv · 2408.01740

Boundary null controllability of the heat equation with Wentzell boundary condition and Dirichlet control

S. E. Chorfi·M. I. Ismailov·L. Maniar·I. Öner
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Abstract

We consider the linear heat equation with a Wentzell-type boundary condition and a Dirichlet control. Such a boundary condition can be reformulated as one of dynamic type. First, we formulate the boundary controllability problem of the system within the framework of boundary control systems, proving its well-posedness. Then we reduce the question to a moment problem. Using the spectral analysis of the associated Sturm-Liouville problem and the moment method, we establish the null controllability of the system at any positive time $T$. Finally, we approximate minimum energy controls by a penalized HUM approach. This allows us to validate the theoretical controllability results obtained by the moment method.

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S. E. Chorfi, M. I. Ismailov, L. Maniar, I. Öner. 2024-08-03. Boundary null controllability of the heat equation with Wentzell boundary condition and Dirichlet control. https://arxiv.org/abs/2408.01740

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