The lack of polynomial stability to mixtures with frictional dissipation

We consider the system modeling a mixture of n materials with frictional damping. We show that the corresponding semigroup is exponentially stable if and only if the imaginary axis is contained in the resolvent set of the infinitesimal generator. In particular this implies the lack of polynomial sta...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 446; no. 2; pp. 1882 - 1897
Main Authors Córdova Puma, Francis F., Muñoz Rivera, Jaime E.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.02.2017
Subjects
Exponential stability
Mixture of materials
Semigroups
Strong stability
Strong stability
Semigroups
Mixture of materials
Exponential stability
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Summary:We consider the system modeling a mixture of n materials with frictional damping. We show that the corresponding semigroup is exponentially stable if and only if the imaginary axis is contained in the resolvent set of the infinitesimal generator. In particular this implies the lack of polynomial stability to the corresponding semigroup.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2016.09.003