Integrally small perturbations of semigroups and stability of partial differential equations
type: Item
instance of: scholarly article
title: Integrally small perturbations of semigroups and stability of partial differential equations
zbMATH Open document ID: 1304.35090
DOI: 10.1155/2013/207581
author: Michael I. Gil'
published in: International Journal of Partial Differential Equations
publication date: 2014-09-30T00:00:00Z
review text: Summary: Let \(A\) be a generator of an exponentially stable operator semigroup in a Banach space, and let \(C(t)\) \((t\geq 0)\) be a linear bounded variable operator. Assuming that \(\int^t_0C(s)ds\) is sufficiently small in a certain sense for the equation \(dx/dt=Ax+C(t)x\), we derive exponential stability conditions. Besides, we do not require that for each \(t_0\geq 0\), the ``frozen'' autonomous equation \(dx/dt=Ax+C(t_0)x\) is stable. In particular, we consider evolution equations with periodic operator coefficients. These results are applied to partial differential equations.
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35L53
Mathematics Subject Classification ID: 47D06
zbMATH DE Number: 6349567
zbMATH Keywords: exponentially stable operator semigroup
zbMATH Keywords: periodic operator coefficients
Wikidata QID: Q58919392
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/207581
OpenAlex ID: W2078912588
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description: scientific article; zbMATH DE number 6349567