Browsing by Author "Abdelaziz Limam"

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    General Decay for a Coupled System of Viscoelastic Wave Equation of Infinite Memory with Acoustic Boundary Conditions
    (Université de M'sila, 2022) Abdelaziz Limam
    coupled system of viscoelastic wave equation of infinite memory is considered. Our system is coupled with the acoustic boundary conditions. Under a very general assumption on the relaxation function, we establish a uniform decay rate. This work substantially improves the earlier results in cases of acoustic boundary conditions. Index Terms—viscoelastic damping, convex functions, general decay
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    Partial Differential Equations and Optimization
    (Université de M'sila, 2022) Abdelaziz Limam
    In this thesis, we consider some viscoelastic problems for a strongly elliptic operator of second order with variable coefficients in bounded domains. A review of the recent studies on the generalized thermoelasticity theories and their associated modified models is also presented. In this regard, we investigate several coupled systems with mixed Dirichlet-Neumann boundary conditions and boundary interaction feedback. The coupling is via the acoustic boundary conditions on a portion of the boundary. Using some interesting methods of mathematical analysis as, semigroup theory, Schauder fixed point, Faedo-Galerkin approach, and compactness estimates, to show the local and global existence of energy-associated solutions. In addition, taking into account the Gearhart-Prüss theorem, the exponential stability of the corresponding semigroup is concluded. Moreover, under a very wider class of generality of relaxation functions, we establish several general decay results using the energy methods