New decay rates for Cauchy problem of the Bresse system in thermoelasticty type III

ABSTRACT

In this paper, we consider the Bresse system in thermoelasticity of type III, we prove new decay results for the $L^2$-norm of the solution and its higher order derivatives. To prove our results, we use the energy method in the Fourier space to build a very delicate Lyapunov functionals that give the desired results. These results improve the one existing in the literature [Said-Houari B, Rahali R. Asymptotic behavior of the Cauchy problem of the Timoshenko system in thermoelsaticity of type III. Evol Equ Control Theory. 2013;2(2):423–440.].

Keywords:

• Bresse system
• thermoelasticity type III
• energy method
• Lyapunov functional

2010 Mathematics Subject Classifications:

• 35Q
• 47F
• 93D

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The author Abdelaziz Soufyane has been funded during the work on this paper by University of Sharjah under Project # 1802144069.