Haak, B. H., Jacob, B., Partington, J. R. and Pott, S. (2009) Admissibility and controllability of diagonal Volterra equations with scalar inputs. Journal of Differential Equations, 246(11), pp. 4423-4440. (doi: 10.1016/j.jde.2009.02.004)
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Abstract
This article studies Volterra evolution equations from the point of view of control theory, in the case that the generator of the underlying semigroup has a Riesz basis of eigenvectors. Conditions for admissibility of the system's control operator are given in terms of the Carleson embedding properties of certain discrete measures. Moreover, exact and null controllability are expressed in terms of a new interpolation question for analytic functions, providing a generalization of results known to hold for the standard Cauchy problem. The results are illustrated by examples involving heat conduction with memory.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Partington, Prof Jonathan and Pott, Dr Sandra |
| Authors: | Haak, B. H., Jacob, B., Partington, J. R., and Pott, S. |
| Subjects: | Q Science > QA Mathematics |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Journal of Differential Equations |
| Publisher: | Elsevier Inc. |
| ISSN: | 0022-0396 |
| ISSN (Online): | 1090-2732 |
| Published Online: | 26 February 2009 |
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