Abstract
This work is devoted to discussing that how the locations of the thermal and viscous damping affect the stability of the 1-d elastic systems. The spatial domain of the 1-d thermoelastic system under consideration can be divided into three sub-intervals, that is, the thermoelastic region of type II, the one of type II with viscous damping, and the one of type III. The following two kinds of energy decay rates for the system are obtained:1.If the thermoelastic region of type III includes one exterior point of the spatial domain of the system, the energy of the system decays exponentially;2.If not, that is the thermoelastic region of type III is strictly inside the spatial domain, the system always lacks of exponential decay. However, the optimal polynomial decay rate is further estimated for this system with smooth initial states. Finally, some numerical simulations are presented to verify the stability results obtained in this work.
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