Titre :	Study Of The Asymptotic Analysis Of Non-Newtonian Flow Models Under Boundary Conditions Formulated In Variable-Exponent Sobolev Frameworks
Type de document :	document électronique
Auteurs :	Rayenne Mebarki, Auteur ; Hamid Benseridi, Directeur de thèse
Editeur :	Sétif:UFS
Année de publication :	2026
Importance :	1 vol (53 f.)
Format :	29 cm
Note générale :
Langues :	Anglais (eng)
Catégories :	Mathématique
Mots-clés :	Convergence analysis Elastic system Source term Thin domain Tresca friction Variable exponents Weak solution
Résumé :	In this Masters thesis, we investigate the asymptotic behavior of a Herschel-Bulkley fluid , assumed to be stationary, incompressible, and isothermal, within a bounded three-dimensional domain. The model incorporates a perturbation term of the form uru and is subject to various boundary conditions, all studied in the framework of variable-exponent Sobolev spaces. After introducing the variational formulation, we apply a scaling transformation of the type z = x3 ε , which converts the original ε-dependent domain into a fixed geometric configuration. This transformation enables us to derive a priori estimates for the velocity and pressure, and to establish an appropriate convergence result. The work concludes with the analysis of the associated limit problem obtained as ε ! 0, for which the uniqueness of the solution is demonstrated.
Note de contenu :	Abstract i General Introduction iii Objectives v 1 Mathematical Preliminaries and Functional Framework 4 1.1 Functional Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.1 Lebesgue Spaces Theory . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.2 Sobolev Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.2.1 Sobolev Space with Zero Boundary . . . . . . . . . . . . 7 1.1.2.2 Weak Convergence in Sobolev Spaces . . . . . . . . . . . 8 1.1.3 Variable Exponent Spaces . . . . . . . . . . . . . . . . . . . . . . . 8 1.1.3.1 Variable Exponent Functions . . . . . . . . . . . . . . . . 9 1.1.3.2 Properties of Lp(x)(Ω) . . . . . . . . . . . . . . . . . . . . 11 1.1.3.3 Variable Exponent Sobolev Spaces . . . . . . . . . . . . . 12 1.1.3.4 Variable Exponent Sobolev Space with Zero Boundary . 13 1.1.4 Convergence in Function Spaces . . . . . . . . . . . . . . . . . . . 13 1.1.4.1 Strong Convergence . . . . . . . . . . . . . . . . . . . . . 13 1.1.4.2 Weak Convergence . . . . . . . . . . . . . . . . . . . . . 13 1.1.4.3 Weak Convergence in Sobolev Spaces . . . . . . . . . . . 14 1.1.4.4 Modular Convergence . . . . . . . . . . . . . . . . . . . 14 1.1.4.5 Relations Between Convergences . . . . . . . . . . . . . 14 1.1.5 Important Analytical Tools . . . . . . . . . . . . . . . . . . . . . . 15 1.1.5.1 Monotone Operators . . . . . . . . . . . . . . . . . . . . 15 1.1.5.2 Minty–Browder Theorem . . . . . . . . . . . . . . . . . . 17 2 Mathematical Model and Variational Analysis 18 2.1 Position of the Problem and Notations . . . . . . . . . . . . . . . . . . . . 18 2.1.1 Formulation of the Model . . . . . . . . . . . . . . . . . . . . . . . 19 2.2 Variational formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3 Asymptotic Analysis and Limit Problem 29 3.1 Asymptotic Framework for Problem (Pϵ) . . . . . . . . . . . . . . . . . . 29 3.1.1 Reformulation via Scale Transformation . . . . . . . . . . . . . . . 29 3.1.2 A priori bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2 Convergence results and limit problem . . . . . . . . . . . . . . . . . . . 38 General conclusion 50
Côte titre :	MAM/0838

Study Of The Asymptotic Analysis Of Non-Newtonian Flow Models Under Boundary Conditions Formulated In Variable-Exponent Sobolev Frameworks [document électronique] / Rayenne Mebarki, Auteur ; Hamid Benseridi, Directeur de thèse . - [S.l.] : Sétif:UFS, 2026 . - 1 vol (53 f.) ; 29 cm.

Langues : Anglais (eng)

Catégories :	Mathématique
Mots-clés :	Convergence analysis Elastic system Source term Thin domain Tresca friction Variable exponents Weak solution
Résumé :	In this Masters thesis, we investigate the asymptotic behavior of a Herschel-Bulkley fluid , assumed to be stationary, incompressible, and isothermal, within a bounded three-dimensional domain. The model incorporates a perturbation term of the form uru and is subject to various boundary conditions, all studied in the framework of variable-exponent Sobolev spaces. After introducing the variational formulation, we apply a scaling transformation of the type z = x3 ε , which converts the original ε-dependent domain into a fixed geometric configuration. This transformation enables us to derive a priori estimates for the velocity and pressure, and to establish an appropriate convergence result. The work concludes with the analysis of the associated limit problem obtained as ε ! 0, for which the uniqueness of the solution is demonstrated.
Note de contenu :	Abstract i General Introduction iii Objectives v 1 Mathematical Preliminaries and Functional Framework 4 1.1 Functional Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.1 Lebesgue Spaces Theory . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.2 Sobolev Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.2.1 Sobolev Space with Zero Boundary . . . . . . . . . . . . 7 1.1.2.2 Weak Convergence in Sobolev Spaces . . . . . . . . . . . 8 1.1.3 Variable Exponent Spaces . . . . . . . . . . . . . . . . . . . . . . . 8 1.1.3.1 Variable Exponent Functions . . . . . . . . . . . . . . . . 9 1.1.3.2 Properties of Lp(x)(Ω) . . . . . . . . . . . . . . . . . . . . 11 1.1.3.3 Variable Exponent Sobolev Spaces . . . . . . . . . . . . . 12 1.1.3.4 Variable Exponent Sobolev Space with Zero Boundary . 13 1.1.4 Convergence in Function Spaces . . . . . . . . . . . . . . . . . . . 13 1.1.4.1 Strong Convergence . . . . . . . . . . . . . . . . . . . . . 13 1.1.4.2 Weak Convergence . . . . . . . . . . . . . . . . . . . . . 13 1.1.4.3 Weak Convergence in Sobolev Spaces . . . . . . . . . . . 14 1.1.4.4 Modular Convergence . . . . . . . . . . . . . . . . . . . 14 1.1.4.5 Relations Between Convergences . . . . . . . . . . . . . 14 1.1.5 Important Analytical Tools . . . . . . . . . . . . . . . . . . . . . . 15 1.1.5.1 Monotone Operators . . . . . . . . . . . . . . . . . . . . 15 1.1.5.2 Minty–Browder Theorem . . . . . . . . . . . . . . . . . . 17 2 Mathematical Model and Variational Analysis 18 2.1 Position of the Problem and Notations . . . . . . . . . . . . . . . . . . . . 18 2.1.1 Formulation of the Model . . . . . . . . . . . . . . . . . . . . . . . 19 2.2 Variational formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3 Asymptotic Analysis and Limit Problem 29 3.1 Asymptotic Framework for Problem (Pϵ) . . . . . . . . . . . . . . . . . . 29 3.1.1 Reformulation via Scale Transformation . . . . . . . . . . . . . . . 29 3.1.2 A priori bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2 Convergence results and limit problem . . . . . . . . . . . . . . . . . . . 38 General conclusion 50
Côte titre :	MAM/0838