Fernando A. Gallego, Jaime E. Munoz Rivera
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 in the -norm, whenever the initial data belongs to 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.
Submitted February 17, 2016. Published March 15, 2017.
Math Subject Classifications: 35B35, 35L55, 93D20.
Key Words: Decay rate; heat conduction; Bresse system; thermoelasticity.
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| Fernando A. Gallego |
Centre de Robotique (CAOR), MINES Paristech
PSL Research University, 60 boulevard Saint-Michel
75272 Paris Cedex 06, France
| Jaime E. Muñoz Rivera |
Laboratório de Computução Científica, LNCC
Petrópolis, 25651-070, RJ, Brazil
email: firstname.lastname@example.org, email@example.com
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