  The objective of the present paper is to investigate the decay of solutions
for a laminated Timoshenko beam with interfacial slip in the whole space R
subject to a thermal effect acting only on one component modelled by either
Fourier or Cattaneo law. When the thermal effect is acting via the second or
third component of the laminated Timoshenko beam (rotation angle displacement
or dynamic of the slip), we obtain that both systems, Timoshenko-Fourier and
Timoshenko-Cattaneo systems, satisfy the same polynomial stability estimates in
the L2 -norm of the solution and its higher order derivatives with respect of
the space variable. The decay rate depends on the regularity of the initial
data. In addition, the presence and absence of the regularity-loss type
property are determined by some relations between the parameters of systems.
However, when the thermal effect is acting via the first comoponent of the
system (transversal displacement), a new stability condition is introduced for
both TimoshenkoFourier and Timoshenko-Cattaneo systems. This stability
condition is in the form of threshold between polynomial stability and
convergence to zero. To prove our results, we use the energy method in Fourier
space combined with judicious choices of weight functions to build appropriate
Lyapunov functionals.
