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EnglishAbstract: In this article we fully describe the domain of the infinitesimal generator of the optimal state semigroup which arises in the theory of the linear-quadratic problem for a specific class of boundary control systems. This represents an improvement over earlier work of the authors, joint with Lasiecka, where a set inclusion was established, but not an equality. The key part of the proof of this result developes through appropriate asymptotic estimates that take advantage of the regularity analysis previously performed in the study of the optimization problem, while the powers of positive operators, interpolation and semigroups provide the analytical tools. We also attest to the validity of an assumed relation between two significant parameters in the case of distinct systems of coupled hyperbolic-parabolic partial differential equations which are pertinent to the underlying framework.
On the infinitesimal generator of an optimal state semigroup (arXiv e-Print) / Paolo Acquistapace; Francesca Bucci. - ELETTRONICO. - (2021), pp. 1-24.
| Titolo: | On the infinitesimal generator of an optimal state semigroup (arXiv e-Print) | |
| Anno del Prodotto: | 2021 | |
| Autori di Ateneo: | BUCCI, FRANCESCA (Corresponding) | |
| Autori: | Paolo Acquistapace; Francesca Bucci | |
| Abstract: | Abstract: In this article we fully describe the domain of the infinitesimal generator of the optimal state semigroup which arises in the theory of the linear-quadratic problem for a specific class of boundary control systems. This represents an improvement over earlier work of the authors, joint with Lasiecka, where a set inclusion was established, but not an equality. The key part of the proof of this result developes through appropriate asymptotic estimates that take advantage of the regularity analysis previously performed in the study of the optimization problem, while the powers of positive operators, interpolation and semigroups provide the analytical tools. We also attest to the validity of an assumed relation between two significant parameters in the case of distinct systems of coupled hyperbolic-parabolic partial differential equations which are pertinent to the underlying framework. | |
| Codice ONU Sustainable Development Goals (SDG): | Goal 17: Partnerships for the goals | |
| Appare nelle tipologie: | 5o - Rapporti di ricerca pubblicati |
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| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| arXiv2104.12747v2.pdf | Preprint (Submitted version) | Open Access | Accesso pubblicoVisualizza/Apri |
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