arXiv subjects

Fredy Maglorio Sobrado Suárez

Publications and source records attributed to Fredy Maglorio Sobrado Suárez.

6 recordsLinked to original sources

arXiv2025

A Gevrey class semigroup, exponential decay and Lack of analyticity for a system formed by a Kirchhoff-Love plate equation and the equation of a membrane-like electric network with indirect fractional damping

The emphasis in this paper is on the Coupled System of a Kirchhoff-Love Plate Equation with the Equation of a Membrane-like Electrical Network, where the coupling is of higher order given by the Laplacian of the displacement velocity $γΔu_t$ and the Laplacian of the potential electric field $γΔv_t $, here only one of the equations is conservative, and the other has dissipative properties. The mechanism was dissipative is given by an intermediate damping $(-Δ)^θv_t$ between the potential electric $θ=0$ (frictional damping) and the Laplacian of the electric potential for $θ=1$ (damping Kelvin Voigt). We show that $S(t)=e^{\mathbb{B}t}$ is not analytic for $θ\in [0, 1[$ and analytic for $θ=1$, however $S(t)=e^{\mathbb{B}t}$ decays exponentially for $0\leq θ\leq 1$ and $S(t)$ is of Gevrey sharp class $s>\frac{1}θ$ when the parameter $θ$ lies in the interval $]0,1[$.

math.AP↗

arXiv2025

Analyticity for Double Wall Carbon Nanotubes Modeled as Timoshenko Beams with Kelvin-Voigt and Intermediate Damping

This manuscript studies a model of double-walled carbon nanotubes using two Timoshenko beams which are coupled by the Van der Walls force $(y-u)$. Kelvin-Voigt type dampings $(u_x-v)_{xt}$ and $(y_x-z)_{xt}$ and fractional dampings $(-\partial_{xx})^αv_t$ and $(-\partial_{xx})^βz_t$ in both beams have been considered. We show that our proposed model is well established and that the semigroup associated is exponentially stable and analytical for any $(α, β) \in [0, 1]^2$. As a consequence of this, a result on the analyticity of a Timoshenko System is obtained.

math.AP↗

arXiv2023

Regularity for the Timoshenko system with fractional damping

We study, the Regularity of the Timoshenko system with two fractional dampings $(-Δ)^τu_t$ and $(-Δ)^σψ_t$; both of the parameters $(τ, σ)$ vary in the interval $[0,1]$. We note that ($τ=0$ or $σ=0$) and ($τ=1$ or $σ=1$) the dampings are called frictional and viscous, respectively. Our main contribution is to show that the corresponding semigroup $S(t)=e^{\mathcal{B}t}$, is analytic for $(τ,σ)\in R_A:=[1/2,1]\times[ 1/2,1]$ and determine the Gevrey's class $ν>\dfrac{1}ϕ$, where $ϕ=\left\{\begin{array}{ccc} \dfrac{2σ}{σ+1} &{\rm for} & σ\leq τ,\\\\ \dfrac{2τ}{τ+1} &{\rm for} & τ\leq σ. \end{array}\right.$ \quad and \quad $(τ,σ)\in R_{CG}:= (0,1)^2$.

math.AP↗

arXiv2023

Regularity to Timoshenko's System with Thermoelasticity of Type III with Fractional Damping

The article, presents the study of the regularity of two thermoelastic beam systems defined by the Timoshenko beam model coupled with the heat conduction of Green-Naghdiy theory of type III, both mathematical models are differentiated by their coupling terms that arise as a consequence of the constitutive laws initially considered. The systems presented in this work have 3 fractional dampings: $μ_1(-Δ)^τϕ_t$, $μ_2(-Δ)^σψ_t$ and $K(-Δ)^ξθ_t$, where $ϕ,ψ$ and $θ$ are transverse displacement, rotation angle and empirical temperature of the bean respectively and the parameters $(τ,σ,ξ)\in [0,1]^3$. It is noted that for values 0 and 1 of the parameter $τ$, the so-called frictional or viscous damping will be faced, respectively. The main contribution of this article is to show that the corresponding semigroup $S_i(t)=e^{\mathcal{B}_it}$, with $i=1,2$, is of Gevrey class $s>\frac{r+1}{2r}$ for $r=\min \{τ,σ,ξ\}$ for all $(τ,σ,ξ)\in R_{CG}:= (0, 1)^3$. It is also showed that $S_1(t)=e^{\mathcal{B}_1t}$ is analytic in the region $R_{A_1}:=\{(τ,σ, ξ)\in [\frac{1}{2},1]^3\}$ and $S_2(t)=e^{\mathcal{B}_2t}$ is analytic in the region $R_{A_2}:=\{(τ,σ, ξ)\in [\frac{1}{2},1]^3/ τ=ξ\}$.

math.AP↗

arXiv2023

Regularity of Euler-Bernoulli and Kirchhoff-Love Thermoelastic Plates with Fractional Coupling

I In this work, we present the study of the regularity of the solutions of the abstract system\eqref{Eq1.10} that includes the Euler-Bernoulli($ω=0$) and Kirchoff-Love($ω>0$) thermoelastic plates, we consider for both fractional couplings given by $A^σθ$ and $A^σu_t$, where $A$ is a strictly positive and self-adjoint linear operator and the parameter $σ\in[0,\frac{3}{2}]$. Our research stems from the work of \cite{MSJR}, \cite{OroJRPata2013}, and \cite{KLiuH2021}. Our contribution was to directly determine the Gevrey sharp classes: for $ω=0$, $s_{01}>\frac{1}{2σ-1}$ and $s_{02}> σ$ when $σ\in (\frac{1}{2},1)$ and $σ\in (1,\frac{3}{2})$ respectively. And $s_ω>\frac{1}{4(σ-1)}$ for case $ω>0$ when $σ\in (1,\frac{5}{4})$. This work also contains direct proofs of the analyticity of the corresponding semigroups $e^{t\mathbb{A}_ω}$: In the case $ω=0$ the analyticity of the semigroup $e^{t\mathbb{A}_0}$ occurs when $σ=1$ and for the case $ω>0$ the semigroup $e^{t\mathbb{A}_ω}$ is analytic for the parameter $σ\in[5/4, 3/2]$. The abstract system is given by: \begin{equation}\label{Eq1.10} \left\{\begin{array}{c} u_{tt}+ωAu_{tt}+A^2u-A^σθ=0,\\ θ_t+Aθ+A^σu_t=0. \end{array}\right. \end{equation} where $ω\geq 0$.

math.AP↗

arXiv2022

A Note on the Regularity of Thermoelastic Plates with Fractional Rotational Inertial Force

The present work intends to complement the study of the regularity of the solutions of the thermoelastic plate with rotacional forces. The rotational forces involve the spectral fractional Laplacian, with power parameter $τ\in [0,1]$ ( $γ(-Δ)^τu_{tt}$). Previous research regarding regularity showed that, as for the analyticity of the semigroup $S(t)=e^{\mathbb{B}t}$ for the Euler-Bernoulli Plate($τ=0$) model, the first result was established by Liu and Renardy, \cite{LiuR95} in the case of hinged and clamped boundary conditions, for the case $τ=1$ (Plate Kirchoff-Love) Lasiecka and Triggiani showed, that the semigroup is not differentiable \cite{LT1998, LT2000} and more recently in 2020 Tebou et al.\cite{Tebou2020} showed that for $τ\in (0,\frac{1}{2})$, $S(t)$ is of class Gevrey $s>\frac{2-τ}{2-4τ}$. Our main contribution here is to show that $S(t)$ is of Gevrey class $s>\frac{3-τ}{2-2τ}$ when the parameter $τ$ lies in the interval $[\frac{1}{2},1)$ and also show that $S(t)$ is not analytic for $τ\in (0,1]$ both results for Hinged plate/ Dirichlet temperature boundary conditions.

math.AP↗