Mathématiques

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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.