Decay rates for solutions to thermoelastic Bresse systems of types I and III

Abstract

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) ∩ H^s (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 <i>regularity-loss</i>. The main tool used to prove our results is the energy method in the Fourier space.