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ABSTRACT
In this work, we study the asymptotic behavior of a porous elastic system coupled with the Fourier law. We show that the norm of resolvent operator is limited uniformly along the imaginary axis and we deduce that if the wave propagation speed are equal, then the system achieves exponential stability. On the other hand, if wave propagation speeds are different, then we show that the resolvent operator is not limited uniformly along the imaginary axis. This leads us to conclude that in general the model is polynomially stable.
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Acknowledgements
The authors are grateful to the anonymous referees for the very careful reading and correction of various misprints.
Notes
No potential conflict of interest was reported by the authors.
Additional information
Funding
The first author has been partially supported by the CNPq [grant number 302899/2015-4]; CNPq Grant Universal [project 401769/2016-0]. The second author thanks to PNPD/CAPES for his financial support.