The Cauchy problem of the Bresse system in thermoelasticity of type III

Abstract

In this paper, we consider the Bresse system coupled with the Green and Naghdi type-III theory of heat conduction. We prove that the decay rate of the solution is very slow. In fact, we show that the -norm of the solution decays with the rate of similar to the one obtained for the Timoshenko system in thermoelasticity of type III. Furthermore, we found that the wave speeds of the equations control the decay rate of the solution with respect to the regularity of the initial data. In addition, we prove that the solution enjoys the property of regularity loss.

Keywords:

• Bresse system
• decay rate
• regularity loss

AMS Subject Classifications:

• 35B37
• 35L55

Notes

No potential conflict of interest was reported by the authors.