Global and local versions for a Phong Vu theorem for periodic evolution families in Hilbert spaces

Global and local versions for a Phong Vu theorem for periodic evolution families in Hilbert spaces

A theorem of Gearhart concerning strongly continuous semigroups in Hilbert spaces is extremely useful for stability analysis of concrete equations; see e.g. [20]), and for control theory [27] or [13, page 475]. Phong Vu introduced an equivalent condition in [23]. The aim of this article is to ex...

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Bibliographic Details
Main Authors: Constantin Buse, Lan Thanh Nguyen, Donal O'Regan
Format: Article
Language:English
Published: Texas State University 2018-11-01
Series:Electronic Journal of Differential Equations
Subjects:
Uniform exponential stability
growth bounds
Fourier series
exponentially bounded evolution families of operators
Online Access:http://ejde.math.txstate.edu/Volumes/2018/188/abstr.html
Description
Summary:A theorem of Gearhart concerning strongly continuous semigroups in Hilbert spaces is extremely useful for stability analysis of concrete equations; see e.g. [20]), and for control theory [27] or [13, page 475]. Phong Vu introduced an equivalent condition in [23]. The aim of this article is to extend these results from the autonomous case to time dependent 1-periodic evolution equations in Hilbert spaces. Both cases (continuous and discrete) are analyzed and global and local versions of the Phong Vu theorem are provided.
ISSN:1072-6691

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