On the stability of a double porous elastic system with visco-porous dampings

TL;DR

This paper investigates the stability of a one-dimensional double porosity elastic system with damping, establishing conditions for exponential decay of solutions and improving previous stability results.

Contribution

It introduces two stability numbers and provides new conditions under which the system's solutions decay exponentially, enhancing existing stability analyses.

Findings

Exponential decay occurs when $ ext{chi}_0=0$ and $ ext{chi}_1 eq0$.

Lack of exponential decay when these conditions are not met.

Improves previous stability results in the literature.

Abstract

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}.