arXiv subjects

Fredy M. Sobrado Suárez

Publications and source records attributed to Fredy M. Sobrado Suárez.

3 recordsLinked to original sources

arXiv2023

The regularity of the coupled system between an electrical network with fractional dissipation and a plate equation with fractional inertial rotational

In this work we study a strongly coupled system between the equation of plates with fractional rotational inertial force $κ(-Δ)^βu_{tt}$ where the parameter $0 <β\leq 1$ and the equation of an electrical network containing a fractional dissipation term $δ(-Δ)^θv_t$ where the parameter $0\leq θ\leq 1$, the strong coupling terms are given by the Laplacian of the displacement speed $γΔu_t$ and the Laplacian electric potential field $γΔv_t$. When $β= 1$, we have the Kirchoff-Love plate and when $β= 0$, we have the Euler-Bernoulli plate recently studied in Suárez-Mendes (2022-Preprinter)\cite{Suarez}. The contributions of this research are: We prove the semigroup $S(t)$ associated with the system is not analytic in $(θ,β)\in [0,1]\times(0,1]-\{( 1,1/2)\}$. We also determine two Gevrey classes: $s_1 >\frac{1}{2\max\{ \frac{1-β}{3-β}, \fracθ{2+θ-β}\}}$ for $2\leq θ+2β$ and $s_2> \frac{2(2+θ-β)}θ$ when the parameters $θ$ and $β$ lies in the interval $(0, 1)$ and we finish by proving that at the point $(θ,β)=(1,1/2)$ the semigroup $S(t)$ is analytic and with a note about the asymptotic behavior of $S(t)$. We apply semigroup theory, the frequency domain method together with multipliers and the proper decomposition of the system components and Lions' interpolation inequality.

math.AP↗

arXiv2023

Stability and Regularity for Double Wall Carbon Nanotubes Modeled as Timoshenko Beams with Thermoelastic Effects and Intermediate Damping

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 $βψ_t$ from the first beam of Tymoshenko and the Laplacian of temperature $δθ_{xx}$, where we also consider the damping terms fractionals $γ_1(-\partial_{xx})^{τ_1}ϕ_t$, $γ_2(-\partial_{xx})^{τ_2} y_t$ and $γ_3(-\partial_{xx})^{τ_3} z_t$, where $(τ_1, τ_2, τ_3) \in [0,1]^3$. For this first system we proved that the semigroup $S_1(t)$ associated to system decays exponentially for all $(τ_1 , τ_2 , τ_3 ) \in [0,1]^3$. The second system also has three fractional damping $γ_1(-\partial_{xx})^{β_1}ϕ_t$, $γ_2(-\partial_{xx})^{β_2} y_t$ and $γ_3(-\partial_{xx})^{β_3} z_t$, with $(β_1, β_2, β_3) \in [0,1]^3$. 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 $βψ_{xxt}$ of the first beam of Timoshenko and the Lapacian of the temperature $δθ_{xx}$. For the second system, we prove the exponential decay of $S_2(t)$ for $(β_1, β_2, β_3) \in [0,1]^3$ and also show that $S_2(t)$ admits Gevrey classes $s>(ϕ+1)/(2ϕ)$ for $ϕ=\min\{β_1,β_2,β_3\}, \forall (β_1,β_2,β_3)\in (0,1)^3$, and proving that $S_2(t)$ is analytic when the parameters $(β_1, β_2, β_3) \in [1/2,1]^3$. One of the motivations for this research was the work; Ramos et al. \cite{Ramos2023CNTs}, whose partial results are part of our results obtained for the first system for $(τ_1, τ_2, τ_3) = (0, 0, 0)$.

math.AP↗

arXiv2023

Stability and Regularity the MGT-Fourier Model with Fractional Coupling

In this work, we study the stability and regularity of the system formed by the third-order vibration equation in Moore-Gilson-Thompson time coupled with the classical heat equation with Fourier's law. We consider fractional couplings. He the fractional coupling is given by: $ηA^ϕθ, αηA^ϕu_{tt}$ and $ηA^ϕu_t$, where the operator $A^ϕ$ is self-adjoint and strictly positive in a complex Hilbert space $H$ and the parameter $ϕ$ can vary between $0$ and $1$. When $ϕ=1$ we have the MGT-Fourier physical model, previously investigated, see; 2013\cite{ABMvFJRSV2013} and 2022\cite{DellOroPata2022}, in these works the authors respectively showed that the semigroup $S(t) = e^{t\mathbb{B}}$ associated with the MGT-Fourier model are exponentially stable and analytical. The model abstract of this research is given by: \eqref{Eq1.1}--\eqref{Eq1.3}, we show directly that the semigroup $S(t)$ is exponentially stable for $ϕ\in [0,1]$, we also show that for $ϕ=1$, $S(t)$ is analytic and study of the Gevrey classes of $S(t)$ and we show that for $ϕ\in (\frac{1}{2}, 1)$ there are two families of Gevrey classes: $s_1>2$ when $ϕ\in(1/2,2/3]$ and $s_2>\fracϕ{2ϕ-1}$ when $ϕ\in[2/3,1)$, in the last part of our investigation using spectral analysis we tackled the study of the non-analyticity and lack of Gevrey classes of $S(t)$ when $ϕ\in[0,1/2]$. For the study of the existence, stability, and regularity, semigroup theory is used together with the techniques of the frequency domain, multipliers, and spectral analysis of system, using proprety of the fractional operator $A^ϕ$ for $ϕ\in[0,1]$.

math.AP↗