University Sétif 1 FERHAT ABBAS Faculty of Sciences
Détail de l'auteur
Auteur Oussama Merabet |
Documents disponibles écrits par cet auteur
Ajouter le résultat dans votre panier Affiner la rechercheVariational And Asymptotic Analysis Of Different Boundary Value Problems With Friction And Memory In Thin Domains / Oussama Merabet
Titre : Variational And Asymptotic Analysis Of Different Boundary Value Problems With Friction And Memory In Thin Domains Type de document : document électronique Auteurs : Oussama Merabet, Auteur ; Mustafa Derguine, Directeur de thèse Editeur : Sétif:UFS Année de publication : 2025 Importance : 1 vol (40 f.) Format : 29 cm Langues : Anglais (eng) Mots-clés : Variational
Asymptotic Analysis
Different Boundary
Value Problems
FrictionRésumé : In this thesis, we study the variational formulations and asymptotic behavior of dynamic problems for viscoelastic
materials defined in thin domains involving friction and memory effects. Using a rigid framework of
functional analysis, we successfully transform physical models of partial differential equations into variational
problems, incorporating Tresca-type boundary conditions and dynamic friction laws.
The primary focus of this study was to derive accurate initial approximations and convergence results as
the thickness of the thin domain approaches zero. This allowed us to define a boundary problem characterized
by a generalized Reynolds-type equation, which captures the essential properties of the original problem in
a simplified form.
The analytical techniques used here-including weak convergence, properties of Sobolev spaces, and coercivity
arguments-are not only fundamental to understanding the mathematical structure of viscoelastic
systems but also pave the way for numerical applications in lubrication theory, biomechanics, and the design
of layered materials in engineering.
This work calls for further exploration of numerical methods adapted to these problems, and for extending
the theory to include more complex geometries or more general types of friction and memory behavior.Note de contenu : Table of contents
Table of contents 1
GENERAL INTRODUCTION 2
1 PRELIMINAIRES 4
1.1 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Equations of continuous medium mechanics . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Viscoelastic constitutive law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Frictional contact boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 Functional spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5.1 Some reminders on functional analysis . . . . . . . . . . . . . . . . . . . . . . 7
1.5.2 Reminder on Sobolev spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.6 Spaces of vector-valued functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.7 Gronwall’s lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.8 Properties of lower semi-continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2 Asymptotic Study of a Viscoelastic Dynamic Problem with Short Memory 19
2.1 Introduction and problem statement . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 Variational formulation of the problem 2.1–2.6 . . . . . . . . . . . . . . . . . . . . . 22
2.3 Asymptotic analysis of the problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3.1 Change of domain and variational problem . . . . . . . . . . . . . . . . . . . 26
2.3.2 A priori estimations and convergence results . . . . . . . . . . . . . . . . . . . 27
2.3.3 Limit problem and the Generalized Reynolds equation . . . . . . . . . . . . . 32
2.3.4 Uniqueness of the solution to the limit problem . . . . . . . . . . . . . . . . . 37
Bibliography 40Côte titre : MAM/0820 Variational And Asymptotic Analysis Of Different Boundary Value Problems With Friction And Memory In Thin Domains [document électronique] / Oussama Merabet, Auteur ; Mustafa Derguine, Directeur de thèse . - [S.l.] : Sétif:UFS, 2025 . - 1 vol (40 f.) ; 29 cm.
Langues : Anglais (eng)
Mots-clés : Variational
Asymptotic Analysis
Different Boundary
Value Problems
FrictionRésumé : In this thesis, we study the variational formulations and asymptotic behavior of dynamic problems for viscoelastic
materials defined in thin domains involving friction and memory effects. Using a rigid framework of
functional analysis, we successfully transform physical models of partial differential equations into variational
problems, incorporating Tresca-type boundary conditions and dynamic friction laws.
The primary focus of this study was to derive accurate initial approximations and convergence results as
the thickness of the thin domain approaches zero. This allowed us to define a boundary problem characterized
by a generalized Reynolds-type equation, which captures the essential properties of the original problem in
a simplified form.
The analytical techniques used here-including weak convergence, properties of Sobolev spaces, and coercivity
arguments-are not only fundamental to understanding the mathematical structure of viscoelastic
systems but also pave the way for numerical applications in lubrication theory, biomechanics, and the design
of layered materials in engineering.
This work calls for further exploration of numerical methods adapted to these problems, and for extending
the theory to include more complex geometries or more general types of friction and memory behavior.Note de contenu : Table of contents
Table of contents 1
GENERAL INTRODUCTION 2
1 PRELIMINAIRES 4
1.1 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Equations of continuous medium mechanics . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Viscoelastic constitutive law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Frictional contact boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 Functional spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5.1 Some reminders on functional analysis . . . . . . . . . . . . . . . . . . . . . . 7
1.5.2 Reminder on Sobolev spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.6 Spaces of vector-valued functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.7 Gronwall’s lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.8 Properties of lower semi-continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2 Asymptotic Study of a Viscoelastic Dynamic Problem with Short Memory 19
2.1 Introduction and problem statement . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 Variational formulation of the problem 2.1–2.6 . . . . . . . . . . . . . . . . . . . . . 22
2.3 Asymptotic analysis of the problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3.1 Change of domain and variational problem . . . . . . . . . . . . . . . . . . . 26
2.3.2 A priori estimations and convergence results . . . . . . . . . . . . . . . . . . . 27
2.3.3 Limit problem and the Generalized Reynolds equation . . . . . . . . . . . . . 32
2.3.4 Uniqueness of the solution to the limit problem . . . . . . . . . . . . . . . . . 37
Bibliography 40Côte titre : MAM/0820 Exemplaires (1)
Code-barres Cote Support Localisation Section Disponibilité MAM/0820 MAM/0820 Mémoire Bibliothèque des sciences Anglais Disponible
Disponible
