Volume 27, 2021Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|Number of page(s)||29|
|Published online||01 March 2021|
Regularity analysis for an abstract thermoelastic system with inertial term
Computer Science Department, Stanford University,
2 Department of Mathematics and Statistics, University of Minnesota, Duluth, MN 55812-2496, USA.
3 School of Mathematics, Beijing Institute of Technology, P.R. China.
4 Department of Mathematics, Federal University of Juiz de Fora, CEP 36036-900, Juiz de Fora, MG, Brazil.
* Corresponding author: email@example.com
Accepted: 5 November 2020
In this paper, we provide a complete regularity analysis for the following abstract thermoelastic system with inertial term
where A is a self-adjoint, positive definite operator on a complex Hilbert space H and
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.
Mathematics Subject Classification: 35B65 / 35K90 / 35L90 / 47D03 / 93D05
Key words: Hyperbolic-parabolic equations / analytic semigroup / Gevrey class semigroup / polynomial stability
© EDP Sciences, SMAI 2021
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