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Polynomial stability of operator semigroups
Author(s) -
Bátkai András,
Engel KlausJochen,
Prüss Jan,
Schnaubelt Roland
Publication year - 2006
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200410429
Subject(s) - mathematics , polynomial , resolvent , banach space , bounded function , generator (circuit theory) , operator (biology) , matrix polynomial , spectrum (functional analysis) , bounded operator , pure mathematics , c0 semigroup , mathematical analysis , power (physics) , biochemistry , physics , chemistry , repressor , quantum mechanics , transcription factor , gene
We investigate polynomial decay of classical solutions of linear evolution equations. For bounded strongly continuous semigroups on a Banach space this property is closely related to polynomial growth estimates of the resolvent of the generator. For systems of commuting normal operators polynomial decay is characterized in terms of the location of the generator spectrum. The results are applied to systems of coupled wave‐type equations. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)