论文标题
Euler-Bernoulli和Kirchhoff-Love热弹性板的规律性与分数耦合
Regularity of Euler-Bernoulli and Kirchhoff-Love Thermoelastic Plates with Fractional Coupling
论文作者
论文摘要
在这项工作中，我们介绍了抽象系统解决方案\ eqref {eq1.10}的规律性，其中包括欧拉 - 伯努利（$ω= 0 $）和kirchoff-love（$ω> 0 $）热弹性平板，我们对两个$ a $ a $ a^nist $ a^nimentimation a^quplings a^n quplings a^n quplings a^n qullys a^n quplys a^n quplys a。 [0，\ frac {3} {2}] $中的自我接合线线性操作员和参数$σ\。我们的研究源于\ cite {msjr}，\ cite {orojrpata2013}和\ cite {kliuh2021}的工作。我们的贡献是直接确定Gevrey Sharp类：对于$ω= 0 $，$ s_ {01}> \ frac {1} {1} {2σ-1} $和$ s_ {02}>σ$时$ c {\ frac {1} {1} {2} {2} {2} {2} {2）$ and $ c {2} 分别。和$s_Ω> \ frac {1} {4（σ-1）} $ for case $ω> 0 $当$σ\ in（1，\ frac {5} {4}）$时。这项工作还包含了相应半群的分析性的直接证明$ e^{t \ mathbb {a}_Ω} $是[5/4，3/2] $中的参数$σ\的分析。抽象系统由：\ begin {equination} \ label {eq1.10} \ left \ {\ oken {arnay} {c} u_ {tt}+ωau_{tt}+ω \ end {array} \ right。 \ end {equation}其中$ω\ geq 0 $。
I In this work, we present the study of the regularity of the solutions of the abstract system\eqref{Eq1.10} that includes the Euler-Bernoulli($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 $ω\geq 0$.
