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Analyticity and Riesz basis property of semigroups associated to damped vibrations

Analyticity and Riesz basis property of semigroups associated to damped vibrations Second order equations of the form $$\ddot{z}(t) + A_0z(t) + D\dot{z}(t) = 0$$ are considered. Such equations are often used as a model for transverse motions of thin beams in the presence of damping. We derive various properties of the operator matrix $$\mathcal{A} = \left( {\begin{array}{*{20}c} 0 & I\\ { -A_0 } & { -D}\\ \end{array}} \right)$$ associated with the second order problem above. We develop sufficient conditions for analyticity of the associated semigroup and for the existence of a Riesz basis consisting of eigenvectors and associated vectors of $${\mathcal{A}}$$ in the phase space. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Evolution Equations Springer Journals

Analyticity and Riesz basis property of semigroups associated to damped vibrations

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References (48)

Publisher
Springer Journals
Copyright
Copyright © 2008 by Birkhaueser
Subject
Mathematics; Analysis
ISSN
1424-3199
eISSN
1424-3202
DOI
10.1007/s00028-007-0351-6
Publisher site
See Article on Publisher Site

Abstract

Second order equations of the form $$\ddot{z}(t) + A_0z(t) + D\dot{z}(t) = 0$$ are considered. Such equations are often used as a model for transverse motions of thin beams in the presence of damping. We derive various properties of the operator matrix $$\mathcal{A} = \left( {\begin{array}{*{20}c} 0 & I\\ { -A_0 } & { -D}\\ \end{array}} \right)$$ associated with the second order problem above. We develop sufficient conditions for analyticity of the associated semigroup and for the existence of a Riesz basis consisting of eigenvectors and associated vectors of $${\mathcal{A}}$$ in the phase space.

Journal

Journal of Evolution EquationsSpringer Journals

Published: May 1, 2008

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