Analyticity and Riesz basis property of semigroups associated to damped vibrations

Details Analyticity and Riesz basis property of semigroups associated to damped vibrations Analyticity and Riesz basis property of semigroups associated to damped vibrations

2007-03-09

arxiv.org/abs/math/0703247v1

J. Evol. Eq. (2008)

Mathematics

Spectral Theory

Scientific paper

10.1007/s00028-007-0351-6

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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