TY - JOUR
T1 - Regularity analysis for an abstract thermoelastic system with inertial term
AU - Kuang, Zhaobin
AU - Liu, Zhuangyi
AU - Fernández Sare, Hugo D.
N1 - Publisher Copyright:
© 2021 EDP Sciences, SMAI.
PY - 2021/3/1
Y1 - 2021/3/1
N2 - In this paper, we provide a complete regularity analysis for the following abstract thermoelastic system with inertial term ρutt+lAγu tt+σAu-mAαθ =0, cθt+mAαu t+kAβθ =0, u(0)=u0,ut(0)=v0, θ(0)=θ0, where A is a self-adjoint, positive definite operator on a complex Hilbert space H and (α,β,γ) E=[0,β+12]×[0,1]×[0,1]. It is regarded as the second part of Fernández Sare et al. [J. Diff. Eqs. 267 (2019) 7085-7134]. where the asymptotic stability of this model was investigated. We are able to decompose the region E into three parts where the associated semigroups are analytic, of Gevrey classes of specific order, and non-smoothing, respectively. Moreover, by a detailed spectral analysis, we will show that the orders of Gevrey class are sharp, under proper conditions. We also show that the orders of polynomial stability obtained in Fernández Sare et al. [J. Diff. Eqs. 267 (2019) 7085-7134] are optimal.
AB - In this paper, we provide a complete regularity analysis for the following abstract thermoelastic system with inertial term ρutt+lAγu tt+σAu-mAαθ =0, cθt+mAαu t+kAβθ =0, u(0)=u0,ut(0)=v0, θ(0)=θ0, where A is a self-adjoint, positive definite operator on a complex Hilbert space H and (α,β,γ) E=[0,β+12]×[0,1]×[0,1]. It is regarded as the second part of Fernández Sare et al. [J. Diff. Eqs. 267 (2019) 7085-7134]. where the asymptotic stability of this model was investigated. We are able to decompose the region E into three parts where the associated semigroups are analytic, of Gevrey classes of specific order, and non-smoothing, respectively. Moreover, by a detailed spectral analysis, we will show that the orders of Gevrey class are sharp, under proper conditions. We also show that the orders of polynomial stability obtained in Fernández Sare et al. [J. Diff. Eqs. 267 (2019) 7085-7134] are optimal.
KW - Analytic semigroup
KW - Gevrey class semigroup
KW - Hyperbolic-parabolic equations
KW - Polynomial stability
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U2 - 10.1051/cocv/2020075
DO - 10.1051/cocv/2020075
M3 - Article
AN - SCOPUS:85101961252
SN - 1292-8119
VL - 27
JO - ESAIM - Control, Optimisation and Calculus of Variations
JF - ESAIM - Control, Optimisation and Calculus of Variations
M1 - 2020075
ER -