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TRANSACTIONS ISSUE MATHEMATICS
Article . 2023 . Peer-reviewed
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Article . 2023
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Polynomial stability of a transmission problem with second sound and distributed delay term

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2023Publisher:Global Cooperation and Analytical Research Center Public UnionJournal:TRANSACTIONS ISSUE MATHEMATICS (issn: 2306-2193, eissn: 2617-7900, Copyright policy )
Authors: Douib, Madani; Zitouni, Salah; Djebabla, Abdelhak;

doi: 10.30546/2617-7900.43.1.2023.41

Polynomial stability of a transmission problem with second sound and distributed delay term

Abstract

Summary: In this work, we consider a transmission problem for an elastic-thermoelastic bar with the elastic part being surrounded by two thermoelastic parts in the presence of an infinite distributed delay term. The heat flux of the system is governed by Cattaneo's law. Under suitable assumption on the weight of the delay, we establish the polynomial stability of the solution by introducing a suitable Lyapunov functional.

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Keywords

Asymptotic stability in control theory, Initial-boundary value problems for systems of linear higher-order PDEs, Thermal effects in solid mechanics, transmission problem, Asymptotic behavior of solutions to PDEs, Stabilization of systems by feedback, distributed delay, parabolic-hyperbolic system, polynomial stability, second sound, Stability of dynamical problems in solid mechanics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average