Uniform decay of energy for a porous thermoelasticity system with past history

Abstract

In this paper, we consider a one-dimensional porous thermoelasticity system with past history, which contains a porous elasticity in the presence of a visco-porous dissipation, a macrotemperature effect and temperature difference. We establish the exponential stability of the system if and only if the equations have the same wave speeds, and obtain the energy decays polynomially to zero in the case that the wave speeds of the equations are different.

Keywords:

• Timoshenko system
• exponential decay
• polynomial decay
• past history

AMS Subject Classifications:

• 35B40
• 74Dxx
• 93D20

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was support by the NSFC [grant number 11526164].