Analyticity and Riesz basis property of semigroups associated to damped vibrations

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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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Spectral Theory, Classical Analysis and ODEs, 47A10, 47A70, 34G10, 47D06

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http://salesiana.dossiersoluciones.com/handle/123456789/155274

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0703247
 http://arxiv.org/abs/math/0703247
 J. Evol. Eq. (2008)
 doi:10.1007/s00028-007-0351-6

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arXiv