The stability of some porous systems
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Date
2022-02-09
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Université Badji Mokhtar Annaba
Abstract
In this thesis, we are interested in studying the well posedness and the stability of some linear one-dimensional porous-elastic systems. The Örst is a porous-thermoelastic system with second sound and a distributed delay term acting on the transverse displacement,where the heat áux of the system is governed by Cattaneoís law. The second is a porous elastic system with microtemperatures and varying delay term, and the last is a swelling
porous thermoelastic soils mixture with second sound, where the thermal conduction is given by the theory of Green and Naghdi called hermoelasticity type III.
Under suitable assumptions, we prove the well-posedness of the systems by using semig roups theory. For the stability of these systems, we use a multipliers technique which is based on the construction of a Lyapunov functional equivalent to energy.
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Keywords
SystËme poreux; systËmes poreux gonáÈs; loi de Cattaneo; deuxiËme son; retard distribuÈ; retard variÈ; thÈorie de semi-groupe; stabilitÈ exponentielle; stabilitÈ polynomiale; fonction de Lyapunov