Semigroup Forum

, Volume 95, Issue 1, pp 222–244 | Cite as

Decay rates for delayed abstract thermoelastic systems with Cattaneo law

  • E. M. Ait Benhassi
  • J. E. Benyaich
  • H. Bouslous
  • L. Maniar
Research Article
First Online:
Received:
Accepted:
  • 67 Downloads

Abstract

In this paper we consider a thermoelastic type system with Cattaneo’s law and internal time delay. Under a suitable assumption on the weight of delay, we prove that the exponential stability of this system is reduced to an observability estimate for the corresponding uncontrolled system. The proof of the main results uses the methodology introduced by Haraux (Port Math 46:245–258, 1989) and generalized by Ammari and Tucsnak (ESAIM COCV 6:361–386, 2001). Illustrating example is given.

Keywords

Abstract thermoelastic of second sound Time delay Cattaneo’s law Transfer function Exponential stability Observability inequality Semigroup 
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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • E. M. Ait Benhassi
    • 1
  • J. E. Benyaich
    • 1
  • H. Bouslous
    • 1
  • L. Maniar
    • 1
  1. 1.Faculté des Sciences Semlalia, LMDP, UMMISCO (IRD- UPMC)Université Cadi AyyadMarrakechMorocco

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