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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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

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spelling	doaj-2811bce4d76647c68afa57feaf07754a2020-11-25T02:41:37ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912018-11-012018188,112Global and local versions for a Phong Vu theorem for periodic evolution families in Hilbert spacesConstantin Buse0Lan Thanh Nguyen1Donal O'Regan2 Politehnica Univ. of Timisoara, Romania Western Kentucky Univ., Bowling Green, KY, USA National Univ. of Ireland, Galway, Ireland 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.http://ejde.math.txstate.edu/Volumes/2018/188/abstr.htmlUniform exponential stabilitygrowth boundsFourier seriesexponentially bounded evolution families of operators
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Constantin Buse Lan Thanh Nguyen Donal O'Regan
spellingShingle	Constantin Buse Lan Thanh Nguyen Donal O'Regan Global and local versions for a Phong Vu theorem for periodic evolution families in Hilbert spaces Electronic Journal of Differential Equations Uniform exponential stability growth bounds Fourier series exponentially bounded evolution families of operators
author_facet	Constantin Buse Lan Thanh Nguyen Donal O'Regan
author_sort	Constantin Buse
title	Global and local versions for a Phong Vu theorem for periodic evolution families in Hilbert spaces
title_short	Global and local versions for a Phong Vu theorem for periodic evolution families in Hilbert spaces
title_full	Global and local versions for a Phong Vu theorem for periodic evolution families in Hilbert spaces
title_fullStr	Global and local versions for a Phong Vu theorem for periodic evolution families in Hilbert spaces
title_full_unstemmed	Global and local versions for a Phong Vu theorem for periodic evolution families in Hilbert spaces
title_sort	global and local versions for a phong vu theorem for periodic evolution families in hilbert spaces
publisher	Texas State University
series	Electronic Journal of Differential Equations
issn	1072-6691
publishDate	2018-11-01
description	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.
topic	Uniform exponential stability growth bounds Fourier series exponentially bounded evolution families of operators
url	http://ejde.math.txstate.edu/Volumes/2018/188/abstr.html
work_keys_str_mv	AT constantinbuse globalandlocalversionsforaphongvutheoremforperiodicevolutionfamiliesinhilbertspaces AT lanthanhnguyen globalandlocalversionsforaphongvutheoremforperiodicevolutionfamiliesinhilbertspaces AT donaloregan globalandlocalversionsforaphongvutheoremforperiodicevolutionfamiliesinhilbertspaces
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Global and local versions for a Phong Vu theorem for periodic evolution families in Hilbert spaces

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