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

• Main Authors: Fernando A. Gallego, Jaime E. Munoz Rivera
• Format: Article
• Language: English
• Published: Texas State University 2017-03-01
• Series: Electronic Journal of Differential Equations
• Subjects: Decay rate; heat conduction; Bresse system; thermoelasticity
• Online Access: http://ejde.math.txstate.edu/Volumes/2017/73/abstr.html

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.