Analysis of the Carbon Nanotubes as Coupled Timsohenko Beam System with Maxwell–Cattaneo Thermal Law

The aim of this paper is to investigate the well-posedness and asymptotic analysis of a double-wall carbon nanotubes, modeled as two coupled one-dimensional Timoshenko beams with Maxwell–Cattaneo heat conduction, where the coupling is through the total deflection of the nanotubes and homogeneous mixed Dirichlet–Neumann boundary conditions. First, we demonstrate the well-posedness of the system using the semigroup theory for linear operators. Secondly, we study the asymptotic stability of the system and show that the solution decays exponentially provided the stability numbers are equal to zero. Furthermore, we show that the solution decays polynomially if the stability numbers are not equal zero.