Mathématiques

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Browsing Mathématiques by Author "Bouzettouta, Lamine"

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    Qualitative Study of some Classes of Evolution Problems
    (20 August 1955 university of Skikda, 2025) KAREK, Widad; Bouzettouta, Lamine
    In this thesis, we present our results about the existence and exponential decay of certain classes of evolution problems. The first problem focuses on a one-dimensional Lord-Schulman thermoelastic system coupled with porous damping and time delay. The heat conduction in this type of systems is described by the Lord–Shulman theory. The second problem focuses on the swelling porous system with the Gurtin-Pipkin thermal effect as the only source of damping with delay. In general, the study shows that the dissipation obtained from the Guertin-Pipkin heat law is sufficient to stabilize the system exponentially, regardless of the system parameters. The third problem focuses on a one-dimensional swelling porous-heat system with time-varying delay in a bounded domain under Dirichlet boundary conditions, with thermodiffusion effects and frictional damping. Overall, using the semi-group approach, the variable norm technique of T. Kato, and the appropriate assumptions on the weight of delay, we establish the wellposedness of the considered systems. Then, we show that our systems are exponentially stable by employing an appropriate Lyapunov functional. We point out that our results are achieved without taking into account that we have the equal of speeds
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    Sur la Stabilité de la poutre de Bresse
    (Université 20 Août 1955 -Skikda, 2021) Boulechfar, Selma; Bouzettouta, Lamine
    In this thesis, we studied the stability of some one-dimensional linear thermoelastic Bresse systems where the heat conduction is given by Green and Naghdi theories (ther- moelasticity type III) with the presence of di§erent mechanisms of dissipation. The Örst is a system of Öve hyperbolic partial di§erential equations with three inÖnite memories. The second has the same form as the previous system, but we replaced the three inÖnite memory terms by two Önite memory terms. The last one is a system of four hyperbolic partial di§erential equations with two di§erent damping, they are constant delay and Önite memory. To show the stabilization of these three systems, we use a multipliers method, it is based on the construction of a Lyapunov function L equivalent to energy E of the solu- tions. In the proof, we used the second order energy function to estimate the terms R 1 0 1tx ('x + + l!) dx and R 1 0 2tx ('x + + l!) dx.