Affiliation:
1. Laboratory of Operators Theory and PDEs: Foundations and Applications , Faculty of Exact Sciences , University of El Oued , B.P. 789 El Oued 39000 , Algeria
2. Department of Mathematics and Computer Sciences , Laboratory of Mathematics, Modelisation and Application (LAMMA) , University of Adrar , Adrar , Algeria
Abstract
Abstract
In this paper, we focused on a one-dimensional elastic system with a double porosity structure and frictional damping acting on both porous equations. We introduce two stability numbers
χ
0
{\chi_{0}}
and
χ
1
{\chi_{1}}
and prove that the solution of the system decays exponentially provided that
χ
0
=
0
{\chi_{0}=0}
and
χ
1
≠
0
{\chi_{1}\neq 0}
. Otherwise, we prove the absence of exponential decay. Our results improve the results of [N. Bazarra, J. R. Fernández, M. C. Leseduarte, A. Magaña and R. Quintanilla,
On the thermoelasticity with two porosities: Asymptotic behaviour,
Math. Mech. Solids 24 2019, 9, 2713–2725] and [A. Nemsi and A. Fareh,
Exponential decay of the solution of a double porous elastic system,
Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 83 2021, 1, 41–50].
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