On the stability of the linearized compressible Adiabatic flow through porous media

Abstract

In this work, we focus on the study of the stability of the Linearized compressible Adiabatic flow System (LAS) in one dimension. Thanks to a study focused on the analysis of the spectrum of the associated linear operator, we were able to determine a new result of exponential stability of the solution in two different Hilbert spaces. Numerical experiments are given to confirm the theoretical results obtained.