论文标题
关于具有分数旋转惯性力的热弹性板的规律性的注释
A Note on the Regularity of Thermoelastic Plates with Fractional Rotational Inertial Force
论文作者
论文摘要
目前的工作旨在补充旋转力对热弹性板溶液的规律性的研究。旋转力涉及光谱分数laplacian，功率参数$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表明，半群没有可区分的\ cite {lt1998，lt2000}，而最近在2020年Tebou等人。 $ s> \ frac {2-τ} {2-4τ} $。我们这里的主要贡献是表明$ s（t）$是Gevrey类$ s> \ frac {3-τ} {2-2τ} $当参数$τ$处于间隔$ [\ frac {1} {1} {2} {2}，1）$时，也显示了$ s（t）$ note $ s for $τ\τ\τ°ous/ dife fors/ s fors/ s fors/ s fors/ s fors/ s fors/ f.11] 状况。
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.
