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On the completeness of root vectors generated by systems of coupled hyperbolic equations.
- Source :
-
Mathematische Nachrichten . Sep2014, Vol. 287 Issue 13, p1497-1523. 27p. - Publication Year :
- 2014
-
Abstract
- The paper is the second in a set of two papers, which are devoted to a unified approach to the problem of completeness of the generalized eigenvectors (the root vectors) for a specific class of linear non-selfadjoint unbounded matrix differential operators. The list of the problems for which such operators are the dynamics generators includes the following: ( a) initial boundary-value problem (IBVP) for a non-homogeneous string with both distributed and boundary damping; ( b) IBVP for small vibrations of an ideal filament with a one-parameter family of dissipative boundary conditions at one end and with a heavy load at the other end; this filament problem is treated for two cases of the boundary parameter: non-singular and singular; ( c) IBVP for a three-dimensional damped wave equation with spherically symmetric coefficients and both distributed and boundary damping; ( d) IBVP for a system of two coupled hyperbolic equations constituting a Timoshenko beam model with variable coefficients and boundary damping; ( e) IBVP for a coupled Euler-Bernoulli and Timoshenko beam model with boundary energy dissipation (the model known in engineering literature as bending-torsion vibration model); ( f) IBVP for two coupled Timoshenko beams model, which is currently accepted as an appropriate model describing vibrational behavior of a longer double-walled carbon nanotube. Problems [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0025584X
- Volume :
- 287
- Issue :
- 13
- Database :
- Academic Search Index
- Journal :
- Mathematische Nachrichten
- Publication Type :
- Academic Journal
- Accession number :
- 97807288
- Full Text :
- https://doi.org/10.1002/mana.201000057