Please use this identifier to cite or link to this item: https://doi.org/10.15480/882.4179
Publisher DOI: 10.1007/978-3-030-89397-2_11
Title: Exponential stability of evolutionary equations
Language: English
Authors: Seifert, Christian  
Trostorff, Sascha 
Waurick, Marcus 
Issue Date: 28-Sep-2021
Publisher: Springer
Source: Operator Theory: Advances and Applications 287: 167-188 (2022-01-01)
Abstract (english): 
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.
URI: http://hdl.handle.net/11420/11753
DOI: 10.15480/882.4179
ISBN: 978-3-030-89397-2
978-3-030-89396-5
Institute: Mathematik E-10 
Document Type: Chapter (Book)
License: CC BY 4.0 (Attribution) CC BY 4.0 (Attribution)
Part of Series: Operator theory 
Volume number: 287
Appears in Collections:Publications with fulltext

Files in This Item:
File Description SizeFormat
Seifert2022_Chapter_ExponentialStabilityOfEvolutio.pdfVerlags-PDF353,29 kBAdobe PDFView/Open
Thumbnail
Show full item record

Page view(s)

50
Last Week
1
Last month
checked on Jun 27, 2022

Download(s)

17
checked on Jun 27, 2022

Google ScholarTM

Check

Note about this record

Cite this record

Export

This item is licensed under a Creative Commons License Creative Commons