Stability analysis of an interactive system of wave equation and heat equation with memory

This paper is devoted to the stability analysis of an interaction system comprised of a wave equation and a heat equation with memory, where the hereditary heat conduction is due to Gurtin–Pipkin law or Coleman–Gurtin law. First, we show the strong asymptotic stability of solutions to this system. Then, the exponential stability of the interaction system is obtained when the hereditary heat conduction is of Gurtin–Pipkin type. Further, we show the lack of uniform decay of the interaction system when the heat conduction law is of Coleman–Gurtin type.