arXiv subjects

Filomena Barbosa Rodrigues Mendes

Publications and source records attributed to Filomena Barbosa Rodrigues Mendes.

3 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↗

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

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↗