New stability result for bresse system with dual-phase-lag thermoelasticity

Abstract

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 τ q and τ θ are proposed. By using the multplier method, we prove that the system is dissipative if 2 τ θ > τ q and exponentially stable by introducing a new stability number χ 1 . This result substantially improves earlier results in the literature.