Theoretical analysis reveals polynomial and exponential stability in degenerate wave systems under heat conduction, highlighting how memory laws govern energy decay.
In this paper, we investigate the stabilization of the transmission problem of the degenerate wave equation and the heat equation under the Coleman–Gurtin heat conduction law or Gurtin–Pipkin law with the memory effect. We investigate the polynomial stability of this system when employing the Coleman–Gurtin heat conduction, establishing a decay rate of type . Next, we demonstrate exponential stability in the case when Gurtin–Pipkin heat conduction is applied.
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Akil et al. (2024) studied this question.
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