Global and local versions for a Phong Vu theorem for periodic evolution families in Hilbert spaces
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Date
2018-11-20
Authors
Buse, Constantin
Nguyen, Thanh Lan
O'Regan, Donal
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Uniform exponential stability, Growth bounds, Fourier series, Exponentially bounded evolution families of operators
Citation
Buşe, C., Nguyen, L. T., & O'Regan, D. (2018). Global and local versions for a Phong Vu theorem for periodic evolution families in Hilbert spaces. <i>Electronic Journal of Differential Equations, 2018</i>(188), pp. 1-12.
Rights
Attribution 4.0 International