This work is devoted to the study of the time decay of the one-dimensional thermoelastic Bresse system where the dual-phase-lag heat conduction theory is used to model the heat transfer. In this theory, two relaxation parameters τq and τθ are proposed. By using the multplier method, we prove that the system is dissipative if 2τθ>τq and exponentially stable by introducing a new stability number χ1. This result substantially improves earlier results in the literature.
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Bouraoui et al. (2024) studied this question.
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