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Analyticity and Riesz basis property of semigroups associated to damped vibrations

Birgit Jacob·Carsten Trunk·Monika Winklmeier
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Abstract

Second order equations of the form $z'' + A_0 z + D z'=0$ in an abstract Hilbert space 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 $A$ 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 $A$ in the phase space.

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Birgit Jacob, Carsten Trunk, Monika Winklmeier. 2007-03-09. Analyticity and Riesz basis property of semigroups associated to damped vibrations. https://doi.org/10.1007/s00028-007-0351-6

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