On controllability, observability and stabilizability of the heat equation on discrete graphs
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917227596349440 |
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| author | Münch, Florentin Seifert, Christian Stollmann, Peter Tautenhahn, Martin |
| author_facet | Münch, Florentin Seifert, Christian Stollmann, Peter Tautenhahn, Martin |
| contents | 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 $α$-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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_20594 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On controllability, observability and stabilizability of the heat equation on discrete graphs Münch, Florentin Seifert, Christian Stollmann, Peter Tautenhahn, Martin Optimization and Control Functional Analysis 93B05, 93B07, 05C63, 35K05, 81S07 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 $α$-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. |
| title | On controllability, observability and stabilizability of the heat equation on discrete graphs |
| topic | Optimization and Control Functional Analysis 93B05, 93B07, 05C63, 35K05, 81S07 |
| url | https://arxiv.org/abs/2601.20594 |