On the asymptotic behavior of some porous elastic systems
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Date
2024
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Université Badji Mokhtar Annaba
Abstract
This thesis is devoted to the study of the existence, uniqueness and the asymptotic behavior T The frst system is a one-dimensional swelling porous elastic system with neutral delay of some porous elastic systems. and porous damping acting on the second equation. We prove that the porous damping dissipation is powerful enough to stabilize the system exponentially even in the presence of neutral delay. The second system is a Lord-Shulman porous-elastic system with dissipation due to microtemper- ature effects, where the thermal conduction has a single-phase-lag that acts as a relaxation time. We show that the system is exponentially stable provided that the new stability number χ = 0. Otherwise, we prove the lack of exponential stability under the assumption χ , 0. Furthermore, in the last case, we show that the solution decays polynomially. The fnal system is the same as the preceding system. However, the energy associated with the solution is not required to be positive defnite ξµ = µ . We introduce a stability number χ and prove the exponential decay of the system if χ = 0 is valid. Otherwise, we show that the system decays polynomially. The method we have used for studying the asymptotic behavior of solutions is the multiplier method based on the energy estimate and Lyapunov direct method. Semi-group and Faedo- Galerkin techniques are those used for the study of the existence and uniqueness.
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swelling porous; neutral delay; porous damping; faedo-galerkin
method; lyapunov functional; exponential stability; microtemperature effects; lack of exponential stability; polynomial stability; lord-shulman thermoelasticity; stability number