On the completeness of root vectors generated by systems of coupled hyperbolic equations (Q2929415)

The paper is a continuation of the article by the author [ibid., No. 8--9, 1118--1147 (2011; Zbl 1230.35073)]. The author studies systems of linear hyperbolic equations describing various types of mechanical vibrations. For each case, the second order system is reduced to a first order system in the time variable. This determines a linear nonselfadjoint matrix differential operator ``responsible'' for the dynamics of the system. The author studies its spectral properties; in particular, she finds conditions for the completeness of its root vectors.NEWLINENEWLINESpecific systems studied in the paper are as follows: 1) Timoshenko beam model with variable coefficients and boundary damping; 2) a coupled Euler-Bernoulli and Timoshenko beam model with boundary energy dissipation (the bending-torsion vibration model); 3) vibrations of a long double-walled carbon nanotube.