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Exponential stability of evolutionary equations
Citation Link: https://doi.org/10.15480/882.4179
Publikationstyp
Book Part
Date Issued
2022
Sprache
English
Institut
TORE-DOI
First published in
Number in series
287
Start Page
167
End Page
188
Citation
Operator Theory: Advances and Applications 287: 167-188 (2022)
Publisher DOI
Scopus ID
Publisher
Springer
In this chapter we study the exponential stability of evolutionary equations. Roughly speaking, exponential stability of a well-posed evolutionary equation (∂t,νM(∂t,ν)+A)U=F (∂ t,ν M(∂ t,ν )+A)U=F means that exponentially decaying right-hand sides F lead to exponentially decaying solutions U. The main problem in defining the notion of exponential decay for a solution of an evolutionary equation is the lack of continuity with respect to time, so a pointwise definition would not make sense in this framework. Instead, we will use our exponentially weighted spaces L2,ν(ℝ; H), but this time for negative ν, and define the exponential stability by the invariance of these spaces under the solution operator associated with the evolutionary equation under consideration.
DDC Class
510: Mathematik
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