In this paper we consider a one dimensional elastic system with double porosity structure and with frictional damping in both porous equations. We introduce two stability numbers $\chi_{ 0}$ and $\chi_{ 1}$ and prove that the solution of the system decays exponentially provided that $\chi_{ 0}=0$ and $\chi_{ 1}\neq0.$ Otherwise, we prove the lack of exponential decay. Our results improve the results of \cite{ Bazarra} and \cite{ Nemsi}.
Categories: math.AP