Decay rates for solutions to thermoelastic Bresse systems of types I and III
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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 L2-norm, whenever the initial data belongs to L1 (ℝ) ∩ Hs (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.
CitationGallego, F. A., Muñoz Rivera, J. E. (2017). Decay rates for solutions to thermoelastic Bresse systems of types I and III. Electronic Journal of Differential Equations, 2017(73), pp. 1-26.
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