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In this paper, we investigate the stability of the transmission problem forRayleigh beam model with heat conduction. First, we reformulate our system intoan evolution equation and prove our problem's well-posedness. Next, wedemonstrate the resolvent of the operator is compact in the energy space, thenby using the general criteria of Arendt-Batty, we prove that the thermaldissipation is enough to stabilize our model. Finally, a polynomial energydecay rate has been obtained which depends on the mass densities and themoments of inertia of the Rayleigh beams.

Well-Posedness and Polynomial energy decay rate of a transmission problem for Rayleigh beam model with heat conduction