Double-wall nanotube as vibrational system: Mathematical approach

Academic Article


  • AbstractIn 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.
  • Authors

  • Shubov, Marianna
  • Rojas-Arenaza, Miriam
  • Status

    Publication Date

  • November 10, 2008
  • Has Subject Area


  • Timoshenko system
  • carbon nanotubes
  • compact resolvent
  • dynamics generator
  • matrix differential operator
  • Digital Object Identifier (doi)

    Start Page

  • 1887
  • End Page

  • 1904
  • Volume

  • 31
  • Issue

  • 16