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The Bresse system in thermoelasticity
Author(s) -
SaidHouari Belkacem,
Soufyane Abdelaziz
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3305
Subject(s) - fourier transform , thermal conduction , mathematical analysis , mathematics , heat equation , norm (philosophy) , initial value problem , wave equation , physics , thermodynamics , law , political science
In this paper, we consider the Bresse system coupled with the Fourier law of heat conduction. We prove that the decay rate of the solution is very slow. In fact, we show that the L 2 ‐norm of the solution decays with the rate of (1 + t ) −1/12 similar to the one obtained for the Timoshenko system. In addition, we found that the wave speed of the first two equations still control the decay rate of the solution with respect to the regularity of the initial data. This seems to be the first result dealing with the behavior of the Cauchy problem in the Bresse–Fourier model. Copyright © 2014 John Wiley & Sons, Ltd.