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

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