Polynomial stability of evolution operators in Banach spaces

Polynomial stability of evolution operators in Banach spaces

The paper considers three concepts of polynomial stability for linear evolution operators which are defined in a general Banach space and whose norms can increase not faster than exponentially. Our approach is based on the extension of techniques for exponential stability to the case of polynomial s...

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Main Authors: Megan Mihail, Traian Ceauşu, Magda Luminiţa Ramneanţu
Format: Article
Language:English
Published: AGH Univeristy of Science and Technology Press 2011-01-01
Series:Opuscula Mathematica
Subjects:
evolution operator
polynomial stability
exponential stability
Online Access:http://www.opuscula.agh.edu.pl/vol31/2/art/opuscula_math_3119.pdf
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spelling doaj-333dddb7e8c34541869ae276425b793e2020-11-24T21:34:44ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742011-01-01312279288http://dx.doi.org/10.7494/OpMath.2011.31.2.2793119Polynomial stability of evolution operators in Banach spacesMegan Mihail0Traian Ceauşu1Magda Luminiţa Ramneanţu2Academy of Romanian Scientists, Independenţei 54, Bucharest, 050094, RomaniaDepartament of Mathematics, West University of Timişoara, Bd. V. Parvan, Nr.4, 300223, Timişoara, RomaniaDepartament of Mathematics, West University of Timişoara, Bd. V. Parvan, Nr.4, 300223, Timişoara, RomaniaThe paper considers three concepts of polynomial stability for linear evolution operators which are defined in a general Banach space and whose norms can increase not faster than exponentially. Our approach is based on the extension of techniques for exponential stability to the case of polynomial stability. Some illustrating examples clarify the relations between the stability concepts considered in paper. The obtained results are generalizations of well-known theorems about the uniform and nonuniform exponential stability.http://www.opuscula.agh.edu.pl/vol31/2/art/opuscula_math_3119.pdfevolution operatorpolynomial stabilityexponential stability
collection DOAJ
language English
format Article
sources DOAJ
author Megan Mihail
Traian Ceauşu
Magda Luminiţa Ramneanţu
spellingShingle Megan Mihail
Traian Ceauşu
Magda Luminiţa Ramneanţu
Polynomial stability of evolution operators in Banach spaces
Opuscula Mathematica
evolution operator
polynomial stability
exponential stability
author_facet Megan Mihail
Traian Ceauşu
Magda Luminiţa Ramneanţu
author_sort Megan Mihail
title Polynomial stability of evolution operators in Banach spaces
title_short Polynomial stability of evolution operators in Banach spaces
title_full Polynomial stability of evolution operators in Banach spaces
title_fullStr Polynomial stability of evolution operators in Banach spaces
title_full_unstemmed Polynomial stability of evolution operators in Banach spaces
title_sort polynomial stability of evolution operators in banach spaces
publisher AGH Univeristy of Science and Technology Press
series Opuscula Mathematica
issn 1232-9274
publishDate 2011-01-01
description The paper considers three concepts of polynomial stability for linear evolution operators which are defined in a general Banach space and whose norms can increase not faster than exponentially. Our approach is based on the extension of techniques for exponential stability to the case of polynomial stability. Some illustrating examples clarify the relations between the stability concepts considered in paper. The obtained results are generalizations of well-known theorems about the uniform and nonuniform exponential stability.
topic evolution operator
polynomial stability
exponential stability
url http://www.opuscula.agh.edu.pl/vol31/2/art/opuscula_math_3119.pdf
work_keys_str_mv AT meganmihail polynomialstabilityofevolutionoperatorsinbanachspaces
AT traianceausu polynomialstabilityofevolutionoperatorsinbanachspaces
AT magdaluminitaramneantu polynomialstabilityofevolutionoperatorsinbanachspaces
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