Abdelaziz Limam2022-01-192022-01-192022http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/27693In 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 methodsAcoustic boundary conditions, Exponential stability, General decay, Global existence of solution, Thermoelastic effect, Viscoelastic dampingThesis