http://dspace.univ-relizane.dz/home/handle/123456789/195 2026-10-01T06:49:55Z http://dspace.univ-relizane.dz/home/handle/123456789/1006 Title: Existence Analysis and Discretization of Nonlinear Partial Differential equations Authors: Abed YFRAH Abstract: This thesis investigates three representative wave equations, including one lin- ear and two nonlinear waves equations, with viscoelastic effects under various bound- ary conditions such as dynamic, Neumann, and Dirichlet conditions. The global ex- istence and uniqueness of weak solutions are established using the Faedo-Galerkin method. Energy techniques and the multiplier method are employed to analyze the long-time behavior, leading to exponential energy decay under suitable assump- tions on the nonlinear and viscoelastic terms. For the numerical approximation, the finite element method is used for spa- tial discretization, resulting in semi-discrete schemes, while implicit time-stepping methods construct fully discrete approximations. Optimal a priori error estimates are derived for both semi-discrete and fully discrete schemes, ensuring stability and convergence. Numerical experiments validate the theoretical results and demonstrate the ef-ficiency and accuracy of the proposed methods. Overall, this thesis provides a uni-fiedtheoretical and numerical framework for nonlinear partial differential equa- tions with strong damping and various boundary conditions. 2025-01-01T00:00:00Z http://dspace.univ-relizane.dz/home/handle/123456789/1005 Title: Variational Problem and Maximal Monotone Operators Authors: Ali BERRAILES Abstract: Differential problems and differential inclusions are fundamental topics in applied mathematics, given their close connection to the theory of maximal monotone operators and their pivotal role in the analysis of numerous math- ematical models in various fields. This framework includes the problem of finding the set of zeros for the sum of maximal monotone operators, which forms the basis for a lot of applications in non-linear analysis, optimization, and some theories related of fixed point. This thesis aims to study the problem of finding a set of zeros for the sum of a family of maximal monotone operators, with a focus on develop- ing efficient algorithms and achieving their convergence properties. First, we reviewed the most important algorithms known in the scientific litera- ture for dealing with the case of a single maximal monotone operator, then the case of a sum of maximal monotone operators, presenting the most no- table modifications and improvements proposed by researchers to accelerate convergence and enhance numerical stability. Next, we addressed the funda- mental problem of finding the zeros of a finite family of maximal monotone operators, dividing it into several special cases. In the context of summing two maximal monotone operators, we proposed an improved method for find- ing solutions based on the Yosida approximation, with a theoretical analysis of the method’s properties and a proof of its convergence. We also presented a new algorithm for dealing with the case of The sum of a pair of maximal monotone operators corresponding to a finite family of nonexpansive oper- ators, Demonstrating strong convergence of their Sequences generated by iteration under appropriate conditions. At a later stage, we generalized the study to the case of the sum of a finite family of maximal monotone operators, and proposed a general algo- rithm based on a radial function to compute the zero set of the problem, with a detailed theoretical analysis of its properties and proof of the appropriate convergence results. At the end of the thesis, we addressed the problem of the difference between two maximal periodic effects and proposed a new method for finding their solutions, studying their convergence properties and high- lighting their contribution to expanding the range of possible applications of the theory of maximal monotone operators. The results obtained in this thesis contribute to enriching the literature on algorithms for solving comprehensiveness problems associated with maximal monotone operators and open new horizons for their applications in the fields of nonlinear analysis and mathematical optimization. 2025-01-01T00:00:00Z http://dspace.univ-relizane.dz/home/handle/123456789/988 Title: Existence and Uniqueness of Solutions for Impulsive Fractional Partial Differential Equation Boundary Value Problems with theψ−Caputo Derivative under the Weak Topology. Authors: Zineb BELLABES Abstract: In this thesis, we study existence, uniqueness, and stability results for several classes of fractional differential equations in Banach spaces. We consider initial value problems for sequentialψ-Caputo fractional Langevin equations, boundary value problems involving impulses with power law kernels, a variable order Caputo thermistor model, and variable order Riemann-Liouville boundary value problems with multi-point data. The analysis is carried out in the weak topology framework using the Pettis integral, the De Blasi mea- sure of weak noncompactness, and fixed-point theorems of M¨onch, Schauder, Banach con- traction, and Krasnoselskii. Existence is proved via M¨onch’s theorem, uniqueness via the Banach contraction principle, and generalized Ulam-Hyers-Rassias stability is established. For the variable order thermistor problem, existence and uniqueness are obtained by split- ting the order into piecewise constant subintervals and applying Schauder’s and Banach’s theorems. For the Riemann-Liouville problem, the method of upper and lower solutions combined with Schauder’s theorem yields positive solutions in a fractional Sobolev space. Numerical examples illustrate the theoretical findings 2025-01-01T00:00:00Z http://dspace.univ-relizane.dz/home/handle/123456789/985 Title: EFFET DES DECHETS DE BETON BITUMINEUX SUR LE COMPORTEMENT DU BETON COMPACTE AU ROULEAU Authors: Ali Kouadri Fadhila Abstract: Le béton compacté au rouleau (BCR) présente des performances prometteuses pour les infrastructures routières, mais son utilisation reste limitée en Algérie. Cette étude propose une approche innovante consistant à développer un béton compacté au rouleau à partir de matériaux locaux, en substituant une partie des granulats traditionnels par des déchets de béton bitumineux recyclés. Le double objectif est de promouvoir l'utilisation du BCR comme matériau de revêtement durable, tout en valorisant les déchets de construction afin de réduire les coûts et l'impact environnemental. Nous avons analysé les propriétés physiques, mécaniques et hydrauliques de ces mélanges de béton sous des températures élevées, en mettant un accent particulier sur leur durabilité dans des conditions sévères (telles que l'expositionàl'acide sulfurique, la perméabilité). Ces essais sont déterminants, car ce béton peut être utilisé à proximité des réseaux d'assainissement, où les transferts d'eau et la corrosion chimique constituent des défis majeurs. Une modélisation tridimensionnelle d'un revêtement en béton de ciment rigideàl'aide du logiciel ANSYS 16.0, en introduisant la loi de comportement du béton correspondante dans le code. Cette modélisation aétéréalisée pour plusieurs cas de chargement sur des dalles en béton de ciment. 2025-01-01T00:00:00Z