Large time behaviour for non-simple thermoelasticity with second sound

Abstract

We prove that the non-simple thermoelastic model, with Cattaneo's or Gurtin-Pipkin's law, is indifferent to the presence of the inertial term. That is, considering or not the irrotational term, there is a lack of exponential stability. Additionally, we show that the semigroup is polynomially stable and that the rate of decay of the solution (both optimal) are the same with or without the rotational term.

Keywords

• Exponential stability
• dissipative systems
• thermoelasticity
• hyperbolic models