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arXiv · 2601.20594

On controllability, observability and stabilizability of the heat equation on discrete graphs

Florentin Münch·Christian Seifert·Peter Stollmann·Martin Tautenhahn
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Abstract

We consider linear control problems for the heat equation of the form $\dot f (t) = -Hf (t) + \mathbf{1}_D u (t)$, $f (0) \in \ell_2 (X,m)$, where $H$ is the weighted Laplacian on a discrete graph $(X,b,m)$, and where $D \subseteq X$ is relatively dense. We show cost-uniform $\alpha$-controllability by means of a weak observability estimate for the corresponding dual observation problem. We discuss optimality of our result as well as consequences on stabilizability properties.

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Florentin Münch, Christian Seifert, Peter Stollmann, Martin Tautenhahn. 2026-01-28. On controllability, observability and stabilizability of the heat equation on discrete graphs. https://arxiv.org/abs/2601.20594

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