Polynomial and exponential stability for one-dimensional problem in thermoelastic diffusion theory

Abstract

We consider one-dimensional problem for the thermoelastic diffusion theory and we obtain polynomial decay estimates. Then we show that the solution decays exponentially to zero as time goes to infinity; that is, denoting by E(t) the first-order energy of the system, we show that positive constants C ₀ and c ₀ exist which satisfy E(t) ≤ C ₀ E(0)e ^{−c ₀ t} .

Keywords:

• thermoelastic diffusion
• polynomial stability
• exponential stability

AMS Subject Classifications::

• 35B35
• 74H55

Acknowledgement

The authors would like to thank the reviewer for his critical review and valuable comments which improved the article thoroughly.