| Summary: | In this article, we study the energy decay for the thermoelastic Bresse system
in the whole line with two dissipative mechanisms, given by heat conduction
(Types I and III). We prove that the decay rate of the solutions are very slow.
More precisely, we show that the solutions decay with the rate of
$(1+t)^{-1/8}$ in the $L^2$-norm, whenever the initial data belongs to
$L^1(\mathbb{R}) \cap H^{s}(\mathbb{R})$ for a suitable s.
The wave speeds of propagation have influence on the decay rate with respect
to the regularity of the initial data. This phenomenon is known as
regularity-loss. The main tool used to prove our results is the
energy method in the Fourier space.
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