Browsing by Author "Laoubi, Karima(Directeur de thèse)"

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Optimal stabilization and controllability of some hyperbolic problems subject to kinetic boundary conditions
(Université M'Hamed Bougara Boumerdès : Faculté des Sciences, 2026) Addoun, Rayan Ikram; Laoubi, Karima(Directeur de thèse)
This thesis is devoted to the study of the stability, regularity, and controllability properties of several classes of hyperbolic systems involving memory effects, singular perturbations, and complex boundary interactions. The analysis combines rigorous theoretical investigations with numerical validations in order to better understand the long-term behavior of such systems. The first part focuses on a strongly coupled linear hyperbolic system in which memory is introduced through a fractional operator of order . The control acts on a single component, while the memory parameter significantly influences the system dynamics. Under suitable assumptions, a polynomial decay rate of the energy is established, demonstrating the stabilizing effect of internal memory and its contribution to efficient control mechanisms. The second part investigates a hyperbolic system with a time-dependent singular damping term coupled with a memory operator. Sufficient conditions on the involved parameters are derived to guarantee polynomial stability and to exclude blow-up phenomena. The obtained results provide a deeper understanding of the influence of temporal singularities on the qualitative behavior of solutions and are supported by numerical simulations. The final part addresses a nonlinear wave equation with localized internal damping, a Carathéodory-type nonlinearity, and dynamic Ventcell-Dirichlet boundary conditions incorporating boundary memory effects. Through the construction of suitable Lyapunov functionals and the use of multiplier techniques, exponential decay estimates are obtained, revealing strong stabilization properties and near-optimal controllability despite the presence of nonlinear and boundary interactions. Overall, this work contributes to the advancement of the theory of hyperbolic systems by highlighting the role of memory mechanisms, fractional dynamics, singular damping effects, and boundary phenomena in the stabilization and control of dissipative systems
Stabilization of different evolution problems by internal dynamic controllers
(Université M'Hamed Bougara Boumerdès : Faculté des Sciences, 2026) Barry, kalifia lassana; Laoubi, Karima(Directeur de thèse)
This thesis explores broadly the stabilization of complex dynamic systems by means of internal controllers. Specially, the asymptotic behavior of damped wave ? in an annular domain ? ? ?n, ?? ? 2, bounded by two edges ?0 and ?1 of class ??2. The inner edge ?0 is fasten so as to prevent any movement on this edge (Homogenous Dirichlet condition): ??|?0 = 0. As for the outer edge, the condition typically considered is: ??(??)?????? + ?????? ? ????? = 0, over ?1 × ?+, ?? ? ???(?1) where ?????? represents the acceleration of ?? (presence of kinetic energy), ?? ? 0 parameter allowing the presence\or absence of kinetic energy on ?1, ?? ? ?n normal vector pointing out of ? along ?1, ??? Laplace-Beltrami operator. First of all, we start by the case where ?? > 0. In second position, we analyze the case where ?? = 0. For each case, we firstly demonstrate the existence and uniqueness of the solution by the semigroup method and the stability of each solution by analyzing the released energy over time. This energy analysis reveals a decrease in energy over time, thus suggesting a possible strong stability. For ?? > 0, we show the strong stability of the solution by exploiting the Arendt-Batty theorem combined with a unique continuation result. Then, we show the exponential stability for ?? > 0 (resp. ?? = 0) by a frequency approach of the ? domain (resp. the Nakao method). Finally, we conduct a series of numerical simulations to illustrate this exponential stability.