STABILITY ANALYSIS FOR ABSTRACT THEOMOELASTIC SYSTEMS WITH CATTANEO’S LAW AND INERTIAL TERMS

Zhong Jie Han; Zhaobin Kuang; Qiong Zhang

doi:10.3934/mcrf.2022053

STABILITY ANALYSIS FOR ABSTRACT THEOMOELASTIC SYSTEMS WITH CATTANEO’S LAW AND INERTIAL TERMS

Zhong Jie Han, Zhaobin Kuang, Qiong Zhang^*

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We study the stability of an abstract thermoelastic system, which consists of an abstract elastic equation with or without inertial term and a heat equation of Cattaneo type. A complete analysis is carried out on how the decay rates of the system depend on the parameter region and the so-called “wave speeds”. Specifically, the parameter region for exponential stability of such a system is characterized. Furthermore, optimality of the rate of polynomial decay is obtained under certain conditions. The proofs rely on interpolation inequalities, frequency domain condition for stability, and detailed spectral analysis.

Original language	English
Pages (from-to)	1639-1673
Number of pages	35
Journal	Mathematical Control and Related Fields
Volume	13
Issue number	4
DOIs	https://doi.org/10.3934/mcrf.2022053
Publication status	Published - Dec 2023

Keywords

Cat-taneo law
Thermoelastic system
exponential stability
inertial term
polynomial stability

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abstract = "We study the stability of an abstract thermoelastic system, which consists of an abstract elastic equation with or without inertial term and a heat equation of Cattaneo type. A complete analysis is carried out on how the decay rates of the system depend on the parameter region and the so-called “wave speeds”. Specifically, the parameter region for exponential stability of such a system is characterized. Furthermore, optimality of the rate of polynomial decay is obtained under certain conditions. The proofs rely on interpolation inequalities, frequency domain condition for stability, and detailed spectral analysis.",

keywords = "Cat-taneo law, Thermoelastic system, exponential stability, inertial term, polynomial stability",

author = "Han, {Zhong Jie} and Zhaobin Kuang and Qiong Zhang",

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AU - Han, Zhong Jie

AU - Kuang, Zhaobin

AU - Zhang, Qiong

PY - 2023/12

Y1 - 2023/12

N2 - We study the stability of an abstract thermoelastic system, which consists of an abstract elastic equation with or without inertial term and a heat equation of Cattaneo type. A complete analysis is carried out on how the decay rates of the system depend on the parameter region and the so-called “wave speeds”. Specifically, the parameter region for exponential stability of such a system is characterized. Furthermore, optimality of the rate of polynomial decay is obtained under certain conditions. The proofs rely on interpolation inequalities, frequency domain condition for stability, and detailed spectral analysis.

AB - We study the stability of an abstract thermoelastic system, which consists of an abstract elastic equation with or without inertial term and a heat equation of Cattaneo type. A complete analysis is carried out on how the decay rates of the system depend on the parameter region and the so-called “wave speeds”. Specifically, the parameter region for exponential stability of such a system is characterized. Furthermore, optimality of the rate of polynomial decay is obtained under certain conditions. The proofs rely on interpolation inequalities, frequency domain condition for stability, and detailed spectral analysis.

KW - Cat-taneo law

KW - Thermoelastic system

KW - exponential stability

KW - inertial term

KW - polynomial stability

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JO - Mathematical Control and Related Fields

JF - Mathematical Control and Related Fields

IS - 4

ER -

STABILITY ANALYSIS FOR ABSTRACT THEOMOELASTIC SYSTEMS WITH CATTANEO’S LAW AND INERTIAL TERMS

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