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Robustness of strongly and polynomially stable semigroups

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Robustness of strongly and polynomially stable semigroups. / Paunonen, Lassi.

julkaisussa: Journal of Functional Analysis, Vuosikerta 263, Nro 9, 2012, s. 2555-2583.

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Paunonen, L 2012, 'Robustness of strongly and polynomially stable semigroups', Journal of Functional Analysis, Vuosikerta. 263, Nro 9, Sivut 2555-2583. https://doi.org/10.1016/j.jfa.2012.08.023

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Paunonen, Lassi. / Robustness of strongly and polynomially stable semigroups. Julkaisussa: Journal of Functional Analysis. 2012 ; Vuosikerta 263, Nro 9. Sivut 2555-2583.

Bibtex - Lataa

@article{8e7ff2a663244c3c96f21354c67e9620,
title = "Robustness of strongly and polynomially stable semigroups",
abstract = "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.",
author = "Lassi Paunonen",
note = "Contribution: organisation=mat,FACT1=1<br/>Publisher name: Academic Press",
year = "2012",
doi = "10.1016/j.jfa.2012.08.023",
language = "English",
volume = "263",
pages = "2555--2583",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Elsevier",
number = "9",

}

RIS (suitable for import to EndNote) - Lataa

TY - JOUR

T1 - Robustness of strongly and polynomially stable semigroups

AU - Paunonen, Lassi

N1 - Contribution: organisation=mat,FACT1=1<br/>Publisher name: Academic Press

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

U2 - 10.1016/j.jfa.2012.08.023

DO - 10.1016/j.jfa.2012.08.023

M3 - Article

VL - 263

SP - 2555

EP - 2583

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 9

ER -