Discrete observability of the heat equation on bounded domains. (English) Zbl 0654.93008
The author investigates discrete-time observability for the heat equation. He shows that under some conditions (like continuous-time cases), it is possible to recover uniquely the initial data from measurements that are discrete in time. The conditions under which the initial data is uniquely recoverable depend on the geometry of the underlying domain and conseqently on the spectrum of the associated eigenvalue problem. Several interesting examples are given.
Reviewer: T.Kobayashi
MSC:
| 93B07 | Observability |
| 93C20 | Control/observation systems governed by partial differential equations |
| 35K05 | Heat equation |
| 35P05 | General topics in linear spectral theory for PDEs |
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| [10] | DOI: 10.1137/0313002 · Zbl 0296.93006 · doi:10.1137/0313002 |
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