Papers by Boubakeur MEROUANI
Journal of the Association of Arab Universities for Basic and Applied Sciences, Oct 1, 2012
In this paper we consider the linear Lame´equations in a non homogeneous three-dimensional domain... more In this paper we consider the linear Lame´equations in a non homogeneous three-dimensional domain Q composed of two homogeneous bodies Q + and Q À with the boundary condition: contact without friction-Dirichlet. We first establish the existence and uniqueness results for weak solutions. Then using cylindrical coordinates and assuming that the neighborhood of the edge A is sufficiently small, we give the transcendental equations governing the singular behavior in the spatial case. In the end, applying the results of Merouani (1996), we obtain an explicit description of the singularities for the variational solution of the boundary value problem in the homogeneous case, i.e. the two bodies have the same elasticity coefficients.
This paper is devoted to the numerical study of an eigenvalue problem modeling the torsional mode... more This paper is devoted to the numerical study of an eigenvalue problem modeling the torsional modes in an infinite and axisymmetric elastic layer. In the cylindrical coordinates´Ö Þµ, without , the problem is posed in a semi-infinite strip ª Ê £ • ¢ ℄¼ Ä. For the numerical approximation, we formulate the problem in the bounded domain ª Ê ℄¼ Ê ¢ ℄¼ Ä. To this end, we use the localized finite element method, which links two representations of the solution: the analytic solution in the exterior domain ª ¼ Ê ℄Ê •½ ¢ ℄¼ Ä and the numerical solution in the interior domain ª Ê .
In this work we study a nonlinear problem equation governed by the system of Lamé, is similar exa... more In this work we study a nonlinear problem equation governed by the system of Lamé, is similar example was the partial differential equations,which operates in relativistic quantum mechanics system.We look for the existence and uniqueness of a function u = u(x, t), x ∈ Ω , t ∈ (0, T) solution of the problem.
Generalized And Perturbed LamÈ System
Global Journal of Science Frontier Research, Jun 12, 2013
In this work, we study the existence, the uniqueness and the regularity of the solution for some ... more In this work, we study the existence, the uniqueness and the regularity of the solution for some boundary value problems gouverned by perturbed and generalized dynamical Lame system operator.
In this work, we study the existence, the uniqueness and the regularity of the solution for some ... more In this work, we study the existence, the uniqueness and the regularity of the solution for some boundary value problems gouverned by a perturbed and generalized Lamé system operator.
We consider a mathematical model which describes the steadystate flow of a Herschel-Bulkley fluid... more We consider a mathematical model which describes the steadystate flow of a Herschel-Bulkley fluid whose the consistency and the yield limit depend on the temperature and with mixed boundary conditions, including a frictional boundary condition. We derive a weak formulation of the coupled system of motion and energy equations which consists of a variational inequality for the velocity field. We prove the existence of weak solutions. In the asymptotic limit case of a high thermal conductivity, the temperature becomes a constant solving an implicit total energy equation involving the consistency function and the yield limit.
Analysis of a Class of Frictional Contact Problems for the Bingham Fluid
Mediterranean Journal of Mathematics, Apr 1, 2005
We consider a mathematical model which describes the stationary flow of a Bingham fluid with fric... more We consider a mathematical model which describes the stationary flow of a Bingham fluid with friction. The frictional contact is modeled by a general velocity dependent dissipation functional. We derive a weak formulation of the model which consists in a variational inequality for the velocity field. We establish the existence and uniqueness of the weak solution as well as its
Fixed Point Theory and Algorithms for Sciences and Engineering, Jun 1, 2022
We consider a nonlinear elasticity problem in a bounded domain, its boundary is decomposed in thr... more We consider a nonlinear elasticity problem in a bounded domain, its boundary is decomposed in three parts: lower, upper, and lateral. The displacement of the substance, which is the unknown of the problem, is assumed to satisfy the homogeneous Dirichlet boundary conditions on the upper part, and not homogeneous one on the lateral part, while on the lower part, friction conditions are considered. In addition, the problem is governed by a particular constitutive law of elasticity system with a strongly nonlinear strain tensor. The functional framework leads to using Sobolev spaces with variable exponents. The formulation of the problem leads to a variational inequality, for which we prove the existence and uniqueness of the solution of the associated variational problem.
Fixed Point Theory and Algorithms for Sciences and Engineering
We consider a nonlinear elasticity problem in a bounded domain, its boundary is decomposed in thr... more We consider a nonlinear elasticity problem in a bounded domain, its boundary is decomposed in three parts: lower, upper, and lateral. The displacement of the substance, which is the unknown of the problem, is assumed to satisfy the homogeneous Dirichlet boundary conditions on the upper part, and not homogeneous one on the lateral part, while on the lower part, friction conditions are considered. In addition, the problem is governed by a particular constitutive law of elasticity system with a strongly nonlinear strain tensor. The functional framework leads to using Sobolev spaces with variable exponents. The formulation of the problem leads to a variational inequality, for which we prove the existence and uniqueness of the solution of the associated variational problem.
Les unités de gériatrie au début de l'épidémie du Covid-19 de 2020 en France./ Geriatric units at the beginning of the 2020 COVID-19 epidemic in France
Geriatr Psychol Neuropsychiatr Vieil, Jun 1, 2020
Studia Universitatis Babes-Bolyai Matematica, 2022
The paper deals with a nonlinear elasticity system with nonconstant coefficients. The existence a... more The paper deals with a nonlinear elasticity system with nonconstant coefficients. The existence and uniqueness of the solution of Neumann's problem is proved using Galerkin techniques and monotone operator theory, in Sobolev spaces with variable exponents.
In this article, we study the solutions to Neumann boundary-value problems of Lamé system in a se... more In this article, we study the solutions to Neumann boundary-value problems of Lamé system in a sectorial domains. We study directly this problem , by using trigonometric series, without going through the Airy functions. Results using the Airy function are given in [11].
Several authors have used trigonometric series for describing the solutions to elliptic equations... more Several authors have used trigonometric series for describing the solutions to elliptic equations in a plane sector; for example, the study of the biharmonic operator with different boundary conditions, can be found in [2, 9, 10]. The main goal of this article is to adapt those techniques for the study of Lamé systems in a sector.
Abstract. We consider a mathematical model which describes the steadystate flow of a Herschel-Bul... more Abstract. We consider a mathematical model which describes the steadystate flow of a Herschel-Bulkley fluid whose the consistency and the yield limit depend on the temperature and with mixed boundary conditions, including a frictional boundary condition. We derive a weak formulation of the coupled system of motion and energy equations which consists of a variational inequality for the velocity field. We prove the existence of weak solutions. In the asymptotic limit case of a high thermal conductivity, the temperature becomes a constant solving an implicit total energy equation involving the consistency function and the yield limit. 1.
Let Ω an open bounded domain of IR, with regular boundary Γ.We denote by u = {u1, u2, u3, ...., u... more Let Ω an open bounded domain of IR, with regular boundary Γ.We denote by u = {u1, u2, u3, ...., un} a vector and T a scalar function on Qτ = Ω×]0, τ [ where τ is a finite real number. λ, μ are the Lamé coefficients with λ ≥ 0 , μ > 0, γ > 0 is a constant. Let k > 0 be the coefficient of the termic conductivity.Our problem is to study a similar example was the partial differential equations, which operates in relativistic quantum mechanics. It means a Ω an open bounded domain of R, with regular boundary Γ.We denot by Q the cylinder
Generalized And Perturbed LamÈ System
Global Journal of Science Frontier Research, 2013
In this work, we study the existence, the uniqueness and the regularity of the solution for some ... more In this work, we study the existence, the uniqueness and the regularity of the solution for some boundary value problems gouverned by perturbed and generalized dynamical Lame system operator.
This paper is devoted to the numerical study of an eigenvalue problem modeling the torsional mode... more This paper is devoted to the numerical study of an eigenvalue problem modeling the torsional modes in an infinite and axisymmetric elastic layer. In the cylindr ical coordinates , without , the problem is posed in a semi-infinite strip . For the numerical approximation, we formulate the problem in the bounded domain . To this end, we use the localized finite element method, whic h links two representations of the solution: the analytic solution in the exterior domain and the numerical solution in the interior domain .
This article represents the solution to a plate problem in a plane sector that is simple supporte... more This article represents the solution to a plate problem in a plane sector that is simple supported, as a series. By using appropriate Green’s functions, we establish a biorthogonality relation between the terms of the series, which allows us to calculate the coefficients.
Quelques problèmes aux limites pour le système de Lamé dans un secteur plan
An explicit description of the singular behavior of the weak solutions of some boundary value pro... more An explicit description of the singular behavior of the weak solutions of some boundary value problems for the Lame system (elasticity) in a plane sector is given On donne une description explicite des singularites des solutions faibles de quelques problemes aux limites pour le systeme de Lale dans un secteur plan
Studia Universitatis Babes-Bolyai Matematica, 2021
In this paper, we consider a mixed problem for a nonlinear elasticity system with laws of general... more In this paper, we consider a mixed problem for a nonlinear elasticity system with laws of general behavior. The coefficients of elasticity depends on x meanwhile the density of the volumetric forces depends on the displacement. The main aim of this paper is to apply the Schauder's fixed point theorem and the techniques of topological degree to prove a theorem of the existence and the uniqueness of the solution of the corresponding variational problem.
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Papers by Boubakeur MEROUANI