Options
Sufficient criteria for stabilization properties in Banach Spaces
Citation Link: https://doi.org/10.15480/882.13359
Publikationstyp
Journal Article
Date Issued
2024-04-08
Sprache
English
Author(s)
Chemnitz University of Technology, Ruhr University Bochum, Technische Universität Dortmund, Universität Rostock
TORE-DOI
Volume
96
Issue
2
Article Number
13
Citation
Integral Equations and Operator Theory 96 (2): 13 (2024)
Publisher DOI
Scopus ID
Publisher
Springer
We study abstract sufficient criteria for cost-uniform open-loop stabilizability of linear control systems in a Banach space with a bounded control operator, which build up and generalize a sufficient condition for null-controllability in Banach spaces given by an uncertainty principle and a dissipation estimate. For stabilizability these estimates are only needed for a single spectral parameter and, in particular, their constants do not depend on the growth rate w.r.t. this parameter. Our result unifies and generalizes earlier results obtained in the context of Hilbert spaces. As an application we consider fractional powers of elliptic differential operators with constant coefficients in Lp(Rd) for p∈[1,∞) and thick control sets.
Subjects
35Q93
47N70
93B07
93D20
Banach space
C -semigroups 0
Fractional powers
Null-controllability
Observability estimate
Primary 47D06
Secondary 93B05
Stabilizability
DDC Class
515.3: Differential calculus and equations
Publication version
publishedVersion
Loading...
Name
s00020-024-02762-x.pdf
Size
421.31 KB
Format
Adobe PDF