Abdelfeteh Fareh | Searcharxiv

arXiv2023

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

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 $χ_{0}$ and $χ_{1}$ and prove that the solution of the system decays exponentially provided that $χ_{0}=0$ and $χ_{1}\neq0.$ Otherwise, we prove the lack of exponential decay. Our results improve the results of \cite{Bazarra} and \cite{Nemsi}.

math.AP↗

arXiv2023

On the time behavior of a porous thermoelastic system with only thermal dissipation given by Gurtin-Pipkin law

In the present paper we consider a porous thermoelastic system with only one dissipative mechanism generated by the heat conductivity modelled by the Gurtin-Pipkin thermal law. By the use of a semigroup approach and the Lumer-Phillips theorem we prove the existence of a unique solution. We introduce a stability number $χ_g$ depends on the coefficients of the system, and establish an exponential stability result provided that $χ_g=0$. Otherwise, if $χ_g\ne 0$, we prove the lack of exponential decay. Our result improves and generalizes the previous results in the literature obtained for Fourier's and Cattaneo's laws of thermal conductivity.

math.AP↗