TUTCRIS - Tampereen teknillinen yliopisto

TUTCRIS

Robustness of strongly and polynomially stable semigroups

Tutkimustuotosvertaisarvioitu

Yksityiskohdat

AlkuperäiskieliEnglanti
Sivut2555-2583
JulkaisuJournal of Functional Analysis
Vuosikerta263
Numero9
DOI - pysyväislinkit
TilaJulkaistu - 2012
OKM-julkaisutyyppiA1 Alkuperäisartikkeli

Tiivistelmä

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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