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Titre: Asymptotic Behavior of a General Boundary Problem in Sobolev Spaces With Variable Exponents
Auteur(s): Smail, Meriem Naouel
Mots-clés: Sobolev
Lebesgue spaces
priori estimates
boundary value problem,
monotonic operators
Tresca law
Date de publication: 2025
Résumé: The problem presented in this thesis concerns the study of a boundary value problem that generalizes the Lamé system, with a nonlinear perturbation in a thin three-dimensional domain with Tresca friction. The results obtained consist in proving the existence and uniqueness of the solution for the corresponding variational problem. The method used to achieve these results is based on the theory of monotone operators, Minty-Browder and the theory of variational inequalities. More precisely, we transformed the original problem defined on the domain Dε into a new equivalent one on a fixed domain D independent of ε using a new scale and several inequalities. Finally, we established various estimates and a convergence Theorem and eventually obtained the limit problem with the generalized weak formulations and their uniqueness. The positive point of this work is the existence and uniqueness of solutions, as well as the possibility of studying their asymptotic behavior in the functional framework based on Sobolev spaces with variable exponent.
URI/URL: http://dspace.univ-setif.dz:8888/jspui/handle/123456789/5559
Collection(s) :Mémoires de master

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