Browsing by Author "Khemis, Rabah"

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    Mathematical Study of a Class of PDE and Fractional Derivatives Equations with Application in Images Processing
    (University of 20 August 1955-Skikda, 2022., 2023) Matallah, Hana; Khemis, Rabah
    Les travaux pr´esent´es dans cette th`ese portent sur l’´etude de quelques ´equations aux d´eriv´ees partielles (EDP) de type parabolique, o`u nous donnons la preuve des r´esultats d’existence pour trois probl`emes principaux en utilisant l’approximation de Feado-Galerkin. Sur la premi`ere, nous prouvons l’existence de la solution g´en´eralis´ee pour une classe de syst`eme parabolique quasi lin´eaire avec des conditions aux limites non locales. La seconde est l’´etude d’un syst`eme de diffusion de r´eaction, o`u l’on donne l’existence d’une solution faible globale dans le cas de la positivit´e et les conditions de masse totale sur les fonctions de non-lin´earit´es. Pour le dernier probl`eme, nous proposons une nouvelle approche d’un mod`ele de diffusion de r´eaction d’ordre fractionnaire, qui est bas´e sur le traitement d’images
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    Theoretical and numerical study of stochastic Keller-Segel problem
    (University 20 august 1955-Skikda, 2023) Slimani, Ali; Khemis, Rabah
    In this thesis, we use a system of nonlinear PDEs, or the conventional d-dimensional parabolicparabolic equation, to explain the Keller-Segel chemotaxis model. These PDEs include a convectiondiffusion equation for the cell density and a reaction-diffusion equation for the chemoattractant concentration. The Keller-Segel chemotaxis model explains how the density of a cell population and the concentration of an attractant change over time. This thesis uses a variety of approaches and strategies to investigate the parabolic Keller-Segel equations. In the first, we talk about the biological and mathematical modeling of the phenomenon of chemical entrapment, and we create a non-linear fractional stochastic Keller-Segel model, where we demonstrate the existence and uniqueness and regularity properties of the mild solution to the investigated time- and space-fractional problem and the required results under specific presumptions. We also studied a stochastic chemotaxis Keller-Segel model perturbed with a Gaussian process, where we proved the local and global existence of solutions in time for a nonlinear stochastic Keller-Segel model with zero Dirichlet boundary conditions, and we also studied the phenomenon of the Keller-Segel model coupled with Boussinesq equations. The primary goals of this work are to investigate the global existence and uniqueness of a weak solution of the problem using the Galerkin method. Finally, we studied the numerical solution of one-dimensional Keller-Segel equations via the new homotopy perturbation method.