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Robustness of strongly and polynomially stable semigroups

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Original languageEnglish
Pages (from-to)2555-2583
JournalJournal of Functional Analysis
Issue number9
Publication statusPublished - 2012
Publication typeA1 Journal article-refereed


In this paper we study the robustness properties of strong and polynomial stability of semigroups of operators. We show that polynomial stability of a semigroup is robust with respect to a large and easily identifiable class of perturbations to its infinitesimal generator. The presented results apply to general polynomially stable semigroups and bounded perturbations. The conditions on the perturbations generalize well-known criteria for the preservation of exponential stablity of semigroups. We also show that the general results can be improved if the perturbation is of finite rank or if the semigroup is generated by a Riesz-spectral operator. The theory is applied to deriving concrete conditions for the preservation of stability of a strongly stabilized one-dimensional wave equation.

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Field of science, Statistics Finland

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