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Double‐wall nanotube as vibrational system: Mathematical approach

In this paper, we present a recently developed mathematical model for short double‐wall carbon nanotubes. The model is governed by a system of four hyperbolic equations representing the two Timoshenko beams coupled through the Van der Waals forces. The system is equipped with a four‐parameter family of the boundary conditions and can be reduced to an evolution equation. This equation defines a strongly continuous semi‐group. Spectral properties of the semi‐group generator are presented in the paper. We show that it is an unbounded non‐selfadjoint operator with compact resolvent. Moreover, this operator is a relatively compact perturbation of a certain selfadjoint operator. Copyright © 2008 John Wiley & Sons, Ltd.