Constantin Buse, Lan Thanh Nguyen, Donal O'Regan
Abstract:
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.
Submitted November 7, 2017. Published November 20, 2018.}
Math Subject Classifications: 35B35 47A30, 46A30.
Key Words: Uniform exponential stability; growth bounds; Fourier series;
exponentially bounded evolution families of operators.
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Constantin Buse Politehnica University of Timisoara Department of Mathematics, Piata Victoriei No. 2 300006-Timisoara, Romania email: constantin.buse@upt.ro, constantin.buse@wku.edu |
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Lan Thanh Nguyen Western Kentucky University Department of Mathematics Bowling Green, KY 42101, USA email: lan.nguyen@wku.edu |
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Donal O'Regan National University of Ireland Galway, Ireland email: donal.oregan@nuigalway.ie |
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