Mathématique
URI permanent de cette collectionhttps://dspacee.univ-temouchent.edu.dz/handle/123456789/747
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Item Contrôlabilité et stabilisabilité des systèmes linéaires dans les espaces de Hilbert(2026) BERREZOUK Halima; HARIRI MohammedCe mémoire est consacré à l’étude de la contrôlabilité et de la stabilisabilité des sys- tèmes linéaires dans les espaces de Hilbert. Ces notions occupent une place importante dans la théorie moderne du contrôle, en particulier dans l’étude des systèmes gouvernés par des équations différentielles ordinaires, des équations aux dérivées partielles et des modèles infini-dimensionnels. Dans un premier temps, nous rappelons les notions de base relatives aux espaces de Hilbert, aux opérateurs linéaires bornés et non bornés, aux opérateurs adjoints, aux projecteurs, aux bases hilbertiennes, aux opérateurs compacts et aux semi-groupes for- tement continus. Ces outils permettent de formuler correctement les systèmes d’évolu- tion abstraits. Dans un deuxième temps, nous étudions les systèmes linéaires infini-dimensionnels de la forme x 0 (t) = Ax(t) + Bu(t), t ≥ 0; x(0) = x0, où A est le générateur infinitésimal d’un semi-groupe fortement continu sur un es- pace de Hilbert X, B est l’opérateur de contrôle et u représente la commande. Nous présentons la notion de solution mild, qui est adaptée aux systèmes infini-dimensionnels lorsque les solutions classiques ne sont pas toujours disponibles. Ensuite, nous analysons la contrôlabilité exacte, la contrôlabilité approchée, l’opé- rateur de contrôlabilité, l’espace atteignable et les critères associés. Une attention par- ticulière est accordée à la dualité entre contrôlabilité et observabilité, qui joue un rôle central dans l’étude des équations aux dérivées partielles contrôlées. Enfin, nous abordons la stabilisabilité des systèmes linéaires dans les espaces de Hilbert. Nous présentons la stabilisation forte, la stabilisation exponentielle, la stabi- lisation par retour d’état et quelques critères spectraux. Une application numérique 5 sous MATLAB est proposée afin d’illustrer les notions étudiées à travers une approxi- mation finie-dimensionnelle d’un système gouverné par un opérateur de type Laplacien.Item Contrôle optimal et ses applications(2026) REZOUG Ahlem; Mohammed HARIRIOptimal control is a fundamental area of applied mathematics, situated at the in- tersection of dynamical systems theory, analysis, and optimization. Its objective is to determine a control that allows a system to evolve from an initial state to a desired state while minimizing a cost functional representing, depending on the context, energy expenditure, trajectory error, transfer time, or economic cost. In this thesis, we first present the mathematical foundations necessary for the study of optimal control, including dynamical systems, existence and uniqueness results for solutions, and some notions of convexity. We then formulate the general problem of optimal control by introducing state variables, admissible controls, constraints, and the cost functional. Particular attention is paid to the main theoretical methods in the field, especially Pontryagin’s maximum principle, dynamic programming, the Hamilton- Jacobi-Bellman equation, and linear quadratic control based on the Riccati equation. Finally, a numerical section using MATLAB is devoted to illustrating the theore- tical results on linear and non-linear systems. The simulations obtained demonstrate the effectiveness of the methods studied for stabilizing dynamic systems and improving their performance while limiting the control effort. This work thus highlights the relevance of optimal control both theoretically and in its numerous applications in automation, engineering, economics, and energy systems.Item Existence et stabilité des solutions du problème de Cauchy pour une équation d’ondes dans Rn avec amortissement par dérivée fractionnaire(2026) BRINI Khadidja; BENAISSA AbdelkaderWave equation with fractional derivative in generalized Caputo sense is investigated. In this thesis, we analyze the Cauchy problem in Rn with linear fractional damping (frictional). First, we establish the system’s well-posedness through semi group theory, ensuring the existence and uniqueness of solutions, named the quantitative results. In addition, we show the strong stability of our system, where qualitative results are obtained by applying the general criterion of Arendt and Batty fombined with C0-semi group approach.Item Étude et analyse d’un modèle mathématique de la pêche(2026) SIDI YAKOUB Wafaa; MAMMAR ImaneThis work focuses on the study of bioeconomic models applied to fisheries. We analyze a multi-site fishery model with variable price as well as a model integrating marine protected areas. The study is based on system reduction, equilibrium analysis and their stability.Item Étude mathématique et numérique de l’équation de poisson avec des conditions mixtes(2026) BENABI Anes; BENKHEDDA HananeThis memoir is dedicated to the study and numerical approximation of solutions to the Poisson problem, a fundamental model of elliptic partial differential equations. In a first step, we established the theoretical framework by recalling Green’s formulas and introducing Sobolev spaces, the natural functional framework of variational analysis. We then demonstrated, using the Lax-Milgram theorem, the existence and uniqueness of the weak solution of the problem. In a second step, we developed a numerical approximation using the finite element method on a conforming triangular mesh, studying two types of elements : P1 elements (affine polynomials) and P2 elements (quadratic polynomials). For each, we constructed the canonical basis of shape functions, established the discrete variational problem, and showed that it reduces to solving a linear system AX = b, where the stiffness matrix A is symmetric positive definite, hence invertible.Item Study of Fractional Boundary Value Problems(2026) LARICHI Nafisa; Dr.BEKRI ZouaouiThis work studies two nonlinear fractional boundary value problems involving the Caputo-Katugampola and Riemann-Liouville derivatives; using theorems (Banach Contraction, leray-schauder nonlinear alternative), it establishes existence, uniqueness and nontrivial existence results for the solution.Item Estimation et tests dans les processus de diffusion à dérive non régulière(2025) Djebbour, Khadîdja; BALASKA, LamiaMany natural, economic, and biological phenomena involve random fluctuations that cannot be captured by purely deterministic models. Stochastic differential equations (SDEs) provide a suitable framework by combining drift and diffusion components. This thesis focuses on a diffusion process with proportional delay and non-regular drift. Two main objectives are addressed: estimating the delay parameter via maximum likelihood in the small-diffusion regime, and constructing a simple versus simple parametric test based on the likelihood ratio. Theoretical results, inspired by the works of Ibragimov, Has’minskii, and Kutoyants, are supported by numerical simulations.Item Théorème de Girsanov et Applications(2025) Slimani, fatima zahra; Messabihi, AichaThis thesis explores Girsanov's Theorem and its applications in stochastic processes, focusing on the Ornstein-Uhlenbeck (O-U) process and Itô-Lévy processes. The study begins with foundational concepts of stochastic processes, including Brownian motion, martingales, and Itô calculus. It then rigorously presents Girsanov’s Theorem, which allows changing the probability measure to transform a stochastic process with drift into a driftless one (or vice versa). The applications demonstrate how Girsanov’s Theorem simplifies the analysis of O- U processes (used in finance and physics) and Itô-Lévy processes (incorporating jumps). Simulations in R illustrate the theoretical results, highlighting the theorem’s utility in financial modeling and risk-neutral pricing.Item Les Séries Stationnaires Appliquées(2025) BOUCHETA, Anissa; BENNAFLA, DjamilaThis thesis aims to study stationary time series, with a particular focus on their properties, identification, modelling, and forecasting. Emphasis will be placed on the application of these methods in specific domains. The project will include a practical analysis of real-world data and an implementation using R.Item Analyse d’un réseau de file d’attente sous des disciplines de service avec priorité(2025) Yekhlef, Hadjer; SAKHI, HananeIn this work, we study the stabilization of a queueing network model under service disciplines with priority; a multi-class fluid queueing system with priority consisting of N stations (N ≥ 3) and 2N classes (each station accommodates two classes). We base our stability analysis on the fluid model.Item Prévision des Séries Chronologiques à l’aide de la Régression Linéaire(2025) OURRAG, Nourhane Keltoum; BENNAFLA, DjamilaThis thesis explores the use of linear regression for time series forecasting. We analyze real-world time series data and implement linear regression techniques to predict future values. We pay special attention to data analysis, model diagnostics, and the evaluation of predictive performance. We also include practical examples and simulations using R, enabling the reader to understand the concepts and apply the presented methods.Item COMPORTEMENT ASYMPTOTIQUE D’UN MODÈLE D’HÉROÏNE AVEC LE TRAITEMENT ÂGE(2020) GASMI, Hadjira; BENTOUT, SoufianeItem ANALYSE MATHÉMATIQUE D’UN MODÈLE ÉPIDÉMIOLOGIQUE(2020) SELLAK, selima; BOUKHALFA, FatemaItem Existence de Solutions pour un Probleme Non Lineaire d’une Equation Differentielle Fractionnaire Implicite(2020) TAHRAOUI, Safaâ; Mami, Tawfiq FawziThe main objective of this paper is to study the existence of solutions for a nonlinear problem of an implicit fractional differential equation. The derivatives considered are in the sense of Caputo and of order between 0 and 1 in a Banach space with boundary conditions and in the second case with non-local ones. These results were obtained by applying the fixed point theory. Examples are included to illustrate the applicability of theoretical results.Item ÉTUDE DE BIFURCATION APPLIQUÉE AUX MODÈLES MATHÉMATIQUES EN SCIENCES(2020) BELOUADI, Khadidja Maroua; BELATTAR, ZokhaThe objective of this thesis is the theoretical and qualitative study of mathematical models applied to science, using some type of bifurcation, we are interested in examining the bifurcation P-A-H and bifurcation cusp theoretically.Item Equations différentirlles d’ordre fractionnaire sur les échelles de temps(2020) BERRAFA, HANANE; LADRANI, Fatima ZohraItem QUELQUES PROBLÈMES DE CAUCHY POUR LES ÉQUATIONS DIFFÉRENTIELLES NON-LINÉAIRES(2020) BOUBOSSELA, Wassila; BIROUD, Kheir eddineIn this memory,we focus on the existence of solution for a nonlinear boundary problem of third and fourth differential equations using the method of upper and lower solutions and some fixed point theorems like Larey Schauder theorem and Guo-Krasnosel’skii and expansion of cones. .Item Fonctions presque périodiques et équations différentielles(2020) raoui, fatna; TCHOUAR, FatimaItem CALCUL rFRACTIONNAIRE CONFORMABLE SUR LES ÉCHELLES DE TEMPS(2020)In this memory , we introduce the definition of nabla conformable fractional derivative of order 2]0; 1] and their important properties , we introduce and develop the notion of nabla conformable fractional integral of order 2]0; 1] on time scales . The basic tools for fractional differentiation and fractional integration are then developed . The Hilger time scale calculus is obtained as a particular case , by choosing = 1 . Many basic properties of the theory are proved .Item DÉRIVATION FRACTIONNAIRE APPLIQUÉE À L’ÉTUDE DE DEUX PROBLÈMES DIFFÉRENTIELS FRACTIONNAIRES NON-LINÉAIRES(2020) MEGTAITI, Sihem; HAMMOUDI, AhmedThe principle of fractional derivation has many applications. It intervenes in the resolution of several nonlinear fractional problems in particular, in the study of existence and uniqueness. This paper discusses different appliquations of this principle as well as some of its extensions and generalizations that involve in the resolution of nonlinear fractional differential problems.We demonstrate the existence and uniqueness of solutions using the principle of Banach contactions and the fixed point theorems of Schaefer and Kranoselskii.