论文标题
具有III型热弹性的Timoshenko系统的规律性，分数阻尼
Regularity to Timoshenko's System with Thermoelasticity of Type III with Fractional Damping
论文作者
论文摘要
该文章介绍了由Timoshenko光束模型定义的两个热弹性光束系统的规律性以及绿色naghdiy III型理论的热传导，这两种数学模型都取决于其耦合术语，这些耦合项是由于最初考虑的构造定律而产生的。这项工作中介绍的系统具有3个分数阻尼：$μ_1（-Δ）^τϕ_t $，$μ_2（-Δ）^σψ_t$和$ k（-Δ）^ξθ_t$，其中$ ϕ，ψ$和$θ$是横向位移的角度，旋转角度和em ement $ nesty camine uncominty an [0,1]^3 $。注意到，对于参数$τ$的值0和1，将分别面对所谓的摩擦或粘性阻尼。本文的主要贡献是表明，相应的半群$ s_i（t）= e^{\ Mathcal {b} _it} $，带有$ i = 1,2 $，是Gevrey class $ s> \ s> \ frac {r+1} $（τ，σ，ξ）\在r_ {cg}中：=（0，1）^3 $。还表明$ s_1（t）= e^{\ mathcal {b} _1t} $在区域中是分析性的$ r_ {a_1}：= \ {（τ，σ，σ，σ，ξ）\ in [\ frac {1} $ s_2（t）= e^{\ mathcal {b} _2T} $在区域中分析$ r_ {a_2}：= \ {（τ，σ，σ，σ）
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 $R_{A_2}:=\{(τ,σ, ξ)\in [\frac{1}{2},1]^3/ τ=ξ\}$.
