Eintrag in der Universitätsbibliographie der TU Chemnitz
Volltext zugänglich unter
URN: urn:nbn:de:bsz:ch1-qucosa2-922082
Bombach, Clemens
Stollmann, Peter (Prof. Dr. rer. nat. habil.) ; Veselić, Ivan (Prof. Dr. rer. nat. habil.) ; Waurick, Marcus (Prof. Dr. rer. nat. habil.) (Gutachter)
Observability inequalities for infinite-dimensional systems in Banach spaces and unique determination of a singular potential from boundary data
Kurzfassung in englisch
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.
| Universität: | Technische Universität Chemnitz | |
| Institut: | Professur Analysis | |
| Fakultät: | Fakultät für Mathematik | |
| Dokumentart: | Dissertation | |
| Betreuer: | Stollmann, Peter (Prof. Dr. rer. nat. habil.) | |
| URL/URN: | https://nbn-resolving.org/urn:nbn:de:bsz:ch1-qucosa2-922082 | |
| SWD-Schlagwörter: | Kontrolltheorie , Harmonische Analyse , Inverses Problem | |
| Freie Schlagwörter (Englisch): | observability estimates , control theory , harmonic analysis , inverse problems | |
| DDC-Sachgruppe: | Mathematik, Analysis, Wahrscheinlichkeiten, angewandte Mathematik | |
| Sprache: | englisch | |
| Tag der mündlichen Prüfung | 22.04.2024 |
