Analyticity and Riesz basis property of semigroups associated to damped vibrations

Jacob, Birgit; Trunk, Carsten GND; Winklmeier, Monika GND

Second order equations of the form z(t)+A0z(t)+D 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 A = 0 I −A0 −D 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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Jacob Prof. Dr., B., Trunk Univ.-Prof. Dr. rer. nat. habil., C., Winklmeier Dr., M., 2007. Analyticity and Riesz basis property of semigroups associated to damped vibrations. Preprint /  Technische Universität Ilmenau, Institut für Mathematik, Preprint /  Technische Universität Ilmenau, Institut für Mathematik 07–19.
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