- Titel
- Observability inequalities for infinite-dimensional systems in Banach spaces and unique determination of a singular potential from boundary data
- Zitierfähige Url:
- https://nbn-resolving.org/urn:nbn:de:bsz:ch1-qucosa2-922082
- Erstveröffentlichung
- 2024
- Datum der Einreichung
- 25.01.2024
- Datum der Verteidigung
- 22.04.2024
- Abstract (EN)
- In this thesis, we prove observability inequalities for systems of differential equations in Banach spaces. In particular, we consider non-autonomous systems and systems of elliptic PDE with infinite-dimensional state space. We employ methods from harmonic analysis. This includes a vector-valued version of the Logvinenko-Sereda theorem, generalizing previous work by O. Kovrijkine. Our results are applied to establish null-controllability of control systems in Banach spaces together with precise estimates on the control cost. Furthermore, we consider an inverse problem for the stationary Schrödinger equation in three dimensions. In this setting, we prove that a Kato-class potential is uniquely determined by it's associated Dirichlet-to-Neumann operator. This complements a result by B. Haberman on the Calderón problem for conductivities with unbounded gradient.
- Freie Schlagwörter (EN)
- observability estimates, control theory, harmonic analysis, inverse problems
- Klassifikation (DDC)
- 510
- 515
- 519
- Normschlagwörter (GND)
- Kontrolltheorie, Harmonische Analyse, Inverses Problem
- GutachterIn
- Prof. Dr. rer. nat. habil. Peter Stollmann
- Prof. Dr. rer. nat. habil. Ivan Veselić
- Prof. Dr. rer. nat. habil. Marcus Waurick
- BetreuerIn Hochschule / Universität
- Prof. Dr. rer. nat. habil. Peter Stollmann
- Den akademischen Grad verleihende / prüfende Institution
- Technische Universität Chemnitz, Chemnitz
- Version / Begutachtungsstatus
- angenommene Version / Postprint / Autorenversion
- URN Qucosa
- urn:nbn:de:bsz:ch1-qucosa2-922082
- Veröffentlichungsdatum Qucosa
- 16.07.2024
- Dokumenttyp
- Dissertation
- Sprache des Dokumentes
- Englisch
- Lizenz / Rechtehinweis
