Titre :	Variational and asymptotic of frictional contact problem for a general operator with friction law in thin domain
Type de document :	texte imprimé
Auteurs :	Yousra Sahraoui, Auteur ; Hamid Benseridi, Directeur de publication, rédacteur en chef
Editeur :	Sétif:UFS
Année de publication :	2024
Importance :	1 vol (55 f.)
Format :	29 cm
Langues :	Anglais (eng)
Catégories :	Thèses & Mémoires:Mathématique
Mots-clés :	priori estimates Boundary value problem Generalized boundary conditions Weak equations Tresca Law Variational formulation
Index. décimale :	510-Mathématique
Résumé :	In this Master's memory, our objective lies on the variational and asymptotic analysis of a nonlinear boundary problem, which theoretically generalizes the Lamé system in a thin 3D domain with friction and generalized boundary condition. To achieve this goal, we first focus on the theoretical study of the weak solution of the presented problem. We then examine the asymptotic behavior as the small parameter ζ approaches zero. Finally, we show different a priori estimates, which will allow us to prove that the problem considered converges in the plan towards a new well-defined problem.
Note de contenu :	Sommaire Dédicaces 5 1 PRELIMINARY FUNCTIONAL ANALYSIS 9 1.1 Lebesgue and normed spaces Lp. . . . . . . . . . . . . . . . . . . . . . . 10 1.2 Sobolev space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.2.1 low convergence and low star convergence . . . . . . . . . . . . . 12 1.2.2 Green formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2.3 Convex and semi-continuous functions below . . . . . . . . . . . 13 1.3 Different inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.3.1 Korn inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.3.2 Poincaré inequality . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.3.3 Hölder inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.3.4 Cauchy-Schwarz inequality . . . . . . . . . . . . . . . . . . . . . . 15 1.3.5 Young inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.4 General information on elliptic variational inequalities (EVI) and their approximations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.4.1 Existence and uniqueness results for the IVE of the first genus 16 1.4.2 Existence and uniqueness results for the IVE of the second genus 18 2 VARIATIONAL STUDY OF AN ELASTIC IN A THIN DOMAIN 20 2.1 Variational formulation of the problem. . . . . . . . . . . . . . . . . . . . 24 2.2 Existence and uniqueness of the weak solution. . . . . . . . . . . . . . 28 3 ASYMPTOTIC STUDY OF PROBLEM Pζ 34 3.1 Asymptotic analysis of the problem Pζ . . . . . . . . . . . . . . . . . . . 35 3.1.1 Problem in transpose form. . . . . . . . . . . . . . . . . . . . . . . 35 3.1.2 A priori estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.2 Convergence results and limit problem . . . . . . . . . . . . . . . . . . . 40
Côte titre :	MAM/0703

Variational and asymptotic of frictional contact problem for a general operator with friction law in thin domain [texte imprimé] / Yousra Sahraoui, Auteur ; Hamid Benseridi, Directeur de publication, rédacteur en chef . - [S.l.] : Sétif:UFS, 2024 . - 1 vol (55 f.) ; 29 cm.
Langues : Anglais (eng)

Catégories :	Thèses & Mémoires:Mathématique
Mots-clés :	priori estimates Boundary value problem Generalized boundary conditions Weak equations Tresca Law Variational formulation
Index. décimale :	510-Mathématique
Résumé :	In this Master's memory, our objective lies on the variational and asymptotic analysis of a nonlinear boundary problem, which theoretically generalizes the Lamé system in a thin 3D domain with friction and generalized boundary condition. To achieve this goal, we first focus on the theoretical study of the weak solution of the presented problem. We then examine the asymptotic behavior as the small parameter ζ approaches zero. Finally, we show different a priori estimates, which will allow us to prove that the problem considered converges in the plan towards a new well-defined problem.
Note de contenu :	Sommaire Dédicaces 5 1 PRELIMINARY FUNCTIONAL ANALYSIS 9 1.1 Lebesgue and normed spaces Lp. . . . . . . . . . . . . . . . . . . . . . . 10 1.2 Sobolev space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.2.1 low convergence and low star convergence . . . . . . . . . . . . . 12 1.2.2 Green formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2.3 Convex and semi-continuous functions below . . . . . . . . . . . 13 1.3 Different inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.3.1 Korn inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.3.2 Poincaré inequality . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.3.3 Hölder inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.3.4 Cauchy-Schwarz inequality . . . . . . . . . . . . . . . . . . . . . . 15 1.3.5 Young inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.4 General information on elliptic variational inequalities (EVI) and their approximations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.4.1 Existence and uniqueness results for the IVE of the first genus 16 1.4.2 Existence and uniqueness results for the IVE of the second genus 18 2 VARIATIONAL STUDY OF AN ELASTIC IN A THIN DOMAIN 20 2.1 Variational formulation of the problem. . . . . . . . . . . . . . . . . . . . 24 2.2 Existence and uniqueness of the weak solution. . . . . . . . . . . . . . 28 3 ASYMPTOTIC STUDY OF PROBLEM Pζ 34 3.1 Asymptotic analysis of the problem Pζ . . . . . . . . . . . . . . . . . . . 35 3.1.1 Problem in transpose form. . . . . . . . . . . . . . . . . . . . . . . 35 3.1.2 A priori estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.2 Convergence results and limit problem . . . . . . . . . . . . . . . . . . . 40
Côte titre :	MAM/0703