Existence and energy decay of a Bresse system with thermoelasticity of type III

In this paper, we investigate a one-dimensional thermoelastic Bresse system, where the heat conduction is given by Green and Naghdi theories. Under some assumptions on the memory kernel and a new introduced stability number, we prove that the unique damping given by the memory term is sufficiently s...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2022-02, Vol.73 (1), Article 3
Main Authors: Djellali, F., Labidi, S., Taallah, F.
Format: Article
Language:English
Subjects:
Conduction heating
Conductive heat transfer
Damping
Decay
Engineering
Mathematical Methods in Physics
Polynomials
Theoretical and Applied Mechanics
Thermoelasticity
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Summary:In this paper, we investigate a one-dimensional thermoelastic Bresse system, where the heat conduction is given by Green and Naghdi theories. Under some assumptions on the memory kernel and a new introduced stability number, we prove that the unique damping given by the memory term is sufficiently strong to stabilize the system exponentially. In fact, we establish a general decay result from which the exponential and polynomial decays are only special cases.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-021-01641-4