Options
Final state observability estimates and cost-uniform approximate null-controllability for bi-continuous semigroups
Citation Link: https://doi.org/10.15480/882.5032
Publikationstyp
Journal Article
Date Issued
2023-03-31
Sprache
English
Author(s)
Institut
TORE-DOI
Journal
Volume
106
Issue
2
Start Page
421
End Page
443
Citation
Semigroup Forum 106 (2): 421-443 (2023-04)
Publisher DOI
Scopus ID
ArXiv ID
Publisher
Springer
Peer Reviewed
true
We consider final state observability estimates for bi-continuous semigroups on Banach spaces, i.e. for every initial value, estimating the state at a final time T>0 by taking into account the orbit of the initial value under the semigroup for t in [0,T], measured in a suitable norm. We state a sufficient criterion based on an uncertainty relation and a dissipation estimate and provide two examples of bi-continuous semigroups which share a final state observability estimate, namely the Gauß–Weierstraß semigroup and the Ornstein-Uhlenbeck semigroup on the space of bounded continuous functions. Moreover, we generalise the duality between cost-uniform approximate null-controllability and final state observability estimates to the setting of locally convex spaces for the case of bounded and continuous control functions, which seems to be new even for the case of Banach spaces.
Subjects
Final state observability estimate
Bi-continuous semigroups
Cost-uniform approximate null-controllability
Saks space
Mixed topology
DDC Class
510: Mathematik
Publication version
publishedVersion
Loading...
Name
Kruse_Seifert_Observability_bi-continuous.pdf
Size
442.33 KB
Format
Adobe PDF