2023/09/10 by Fredy Maglorio Sobrado Suárez, Suárez, Fredy M. Sobrado, Lesly Daiana Barbosa Sobrado +5 · 1 citation
Computer Science · Engineering · Materials Science · #35B65 #35K90 #47D03 #47G10 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlocal and gradient elasticity in micro/nano structures #Thermoelastic and Magnetoelastic Phenomena
paper · pdf · doi:10.48550/arxiv.2309.04906
openalex publication_date 2023/09/10 · openalex created_date 2023/09/14 · openalex updated_date 2026/07/28
This research studies two systems composed by the Timoshenko beam model for double wall carbon nanotubes, coupled with the heat equation governed by Fourier's law. For the first system, the coupling is given by the speed the rotation of the vertical filament in the beam βψt from the first beam of Tymoshenko and the Laplacian of temperature δθxx, where we also consider the damping terms fractionals γ1(-∂xx)τ1ϕt, γ2(-∂xx)τ2 yt and γ3(-∂xx)τ3 zt, where (τ1, τ2, τ3) ∈ [0,1]3. For this first system we proved that the semigroup S1(t) associated to system decays exponentially for all (τ1 , τ2 , τ3 ) ∈ [0,1]3. The second system also has three fractional damping γ1(-∂xx)β1ϕt, γ2(-∂xx)β2 yt and γ3(-∂xx)β3 zt, with (β1, β2, β3) ∈ [0,1]3. Furthermore, the couplings between the heat equation and the Timoshenko beams of the double wall carbon nanotubes for the second system is given by the Laplacian of the rotation speed of the vertical filament in the beam βψxxt of the first beam of Timoshenko and the Lapacian of the temperature δθxx. For the second system, we prove the exponential decay of S2(t) for (β1, β2, β3) ∈ [0,1]3 and also show that S2(t) admits Gevrey classes s>(ϕ+1)/(2ϕ) for ϕ=min\β1,β2,β3\, ∀ (β1,β2,β3)∈ (0,1)3, and proving that S2(t) is analytic when the parameters (β1, β2, β3) ∈ [1/2,1]3. One of the motivations for this research was the work; Ramos et al. \citeRamos2023CNTs, whose partial results are part of our results obtained for the first system for (τ1, τ2, τ3) = (0, 0, 0).