M. BENABDERRAHMANE Benyattou

Prof

Directory of teachers

Department

Mathematics Department

Research Interests

Methods of Functional Analysis (Partial differential equations) Applied to Mechanics; Nonlinear Analysis Applied Mathematics

Contact Info

University of M'Sila, Algeria

Email : benyattou.benabderrahmane@univ-msila.dz

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Recent Publications

2021

Global solvability and decay estimates for a type III thermo-viscoelastic coupled system with infinite memory and boundary interaction feedback

A type III thermo-viscoelastic coupled system with infinite memory and distributed delay is considered. The interaction feedback between the nonlinear damping and the acoustic conditions are reacted on portion of the boundary. We obtain the well posedness and regularity of the system by using semigroup theory which is combined with Schauder’s fixed point theorem. Moreover, the general decay estimates are established under a much larger class of relaxation functions. Our results are obtained without the boundedness condition of initial data assumed in many earlier papers in the literature. This work generalizes the composite stability between infinite memory and nonlinear damping.
Citation

M. BENABDERRAHMANE Benyattou, Yamna Boukhatem, , (2021), "Global solvability and decay estimates for a type III thermo-viscoelastic coupled system with infinite memory and boundary interaction feedback", [national] Mathematische Nachrichten , WILEY VCH

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General decay for a coupled system of viscoelastic wave equation of infinite memory with acoustic boundary conditions

A coupled system of viscoelastic wave equation of infinite memory is considered. The coupling is via by the acoustic boundary conditions. Under very general assumption on the relaxation function, we establish a general decay result. This work substantially improves the earlier results in cases of acoustic boundary conditions.
Citation

M. BENABDERRAHMANE Benyattou, Yamna Boukhatem, , (2021), "General decay for a coupled system of viscoelastic wave equation of infinite memory with acoustic boundary conditions", [international] International Conference on Recent Advances in Mathematics and Informatics (ICRAMI 2021) , University of Laarbi Tebessi, Tebessa, Algeria

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General Decay Result for a Type III Thermoelastic Coupled System with Acoustic Boundary Conditions in the Presence of Distributed Delay

In the paper, the general decay of energy solutions for a type III thermoelastic coupled system with distributed delay is studied. The coupling is via the acoustic boundary conditions. Our result is obtained under a class of generality of the relaxation function g : R+ → R+ satisfying the inequality g'(t) ≤ −ξ(t)H(t) for all t ≥ 0, where ξ and H are functions satisfying some specific properties. This work extends previous works with thermoelasticity of type III and improves earlier results in the literature.
Citation

M. BENABDERRAHMANE Benyattou, Yamna Boukhatem, , (2021), "General Decay Result for a Type III Thermoelastic Coupled System with Acoustic Boundary Conditions in the Presence of Distributed Delay", [national] Journal of Mathematical Physics, Analysis, Geometry , National Academy of Sciences of Ukraine, B.Verkin, Institute for Low Temperature Physics and Engineering.

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On a viscoelastic wave equation of infinite memory coupled with acoustic boundary conditions

This work deals with a coupled system of viscoelastic wave equation of infinite memory. The coupling is via by the acoustic boundary conditions. The semigroup theory is used to show the global existence of solution. Moreover, we investigate exponential stability of the system taking into account Gearhart-Pruss’ theorem.
Citation

M. BENABDERRAHMANE Benyattou, Yamna Boukhatem, , (2021), "On a viscoelastic wave equation of infinite memory coupled with acoustic boundary conditions", [international] The First Online International Conference on Pure and Applied Mathematics IC-PAM’21 , Kasdi Merbah University, Ouargla, Algeria

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New general stability for a variable coefficient thermo-viscoelastic-coupled system of second sound with acoustic boundary conditions

In this paper, we consider a variable coefficient thermo-viscoelastic-coupled system of second sound with acoustic boundary conditions, where the heat conduction is given by Cattaneo’s law. We establish a general decay of energy-associated solutions under a class of generality of the relaxation function. Our result extends the various decay results obtained for problems with or without thermo-viscoelasticity.
Citation

M. BENABDERRAHMANE Benyattou, Yamna Boukhatem, , (2021), "New general stability for a variable coefficient thermo-viscoelastic-coupled system of second sound with acoustic boundary conditions", [national] Computational and Applied Mathematics , Springer Nature

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Problèmes de contact avec frottement à coefficient variable: Etude mathématique pour des solides déformables

Considérons deux problèmes hyperboliques semi linéaire avec une source non linéaire de type polynomiale, le premier concerne un problème hyperbolique semi linéaire pour un opérateur fortement elliptique à coefficients variables et avec une dissipation forte et une dissipation non linéaire, tandis que le second est un problème aux limites acoustique pour les équations des ondes viscoélastiques à coefficients variables. Sous certaines conditions sur les données initiales en se basant sur des techniques récentes d’analyse mathématique, des résultats importants sur l’existence locale et globale, l’unicité, comportement asymptotique et l’explosion en temps fini des solutions sont obtenus.
Citation

M. BENABDERRAHMANE Benyattou, (2021), "Problèmes de contact avec frottement à coefficient variable: Etude mathématique pour des solides déformables", [national] , Editions Universitaires Européennes

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2019

Quasilinear parabolic equations with p(x)-Laplacian diffusion terms and nonlocal boundary conditions

In this study, we prove the existence of local solution for a quasi linear generalized parabolic equation with nonlocal boundary conditions for an elliptic operator involving the variable-exponent nonlinearities, using Faedo-Galerkin arguments and compactness method.
Citation

M. BENABDERRAHMANE Benyattou, (2019), "Quasilinear parabolic equations with p(x)-Laplacian diffusion terms and nonlocal boundary conditions", [national] Stud. Univ. Babe¸s-Bolyai Math , Studia Universitatis Babeș-Bolyai Mathematica

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Exponential Stability for a Linear Coupled System of Thermoelastic Type of Second Sound

In this work, we consider a linear coupled system of thermoelastic type with both second sound and acoustic boundary conditions, where the heat conduction is given by Cattaneo's law and the coupling is via the displacement equation. We show the well possedness of the system by using the semigroup theory. Moreover, we investigate with a stability exponential with a PDE technique of a $\mathcal{C}_0-$semigroup on a Hilbert space.
Citation

M. BENABDERRAHMANE Benyattou, Yamna Boukhatem, , (2019), "Exponential Stability for a Linear Coupled System of Thermoelastic Type of Second Sound", [international] Third International Conference in Operator Theory, PDE and Applications (CITO2019) , El Oued, Algeria

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Dynamic total slip-ratedependent frictional contact problem for a nonlinear viscoelastic materials with long memory

In this paper, we consider a mathematical model which describes the dynamic frictional contact between a deformable body and rigid foundation. We assume
that the behavior of the body is described by a nonlinear viscoelastic constitutive law with long memory. The friction condition is modeled with a simpli ed version of Coulomb's
law in which the normal stress is prescribed and the coefficient of friction depends on the total slip-rate. We present the classical formulation of the problem, and derive a varia-
tional formulation which consists a second order evolutionary quasi-variational inequality for the displacement led. Then, we establish the existence and uniqueness result of weak
solution. The proof is based on the Faedo-Galerkin method and Banach's fixed point theorem. Finally, we show a convergence result when the relaxation coefficients of long
memory tend to zero.
Citation

M. BENABDERRAHMANE Benyattou, (2019), "Dynamic total slip-ratedependent frictional contact problem for a nonlinear viscoelastic materials with long memory", [national] Analele Universitatii Oradea. Fasc. Matematica , Universitatii Oradea

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2018

Workshops on Pure and Applied Mathematics, WPAM 2018

Workshops on Pure and Applied Mathematics, WPAM 2018
Citation

M. BENABDERRAHMANE Benyattou, (2018), "Workshops on Pure and Applied Mathematics, WPAM 2018", [national] Workshops on Pure and Applied Mathematics, WPAM 2018 , M'Sila

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Deuxième Workshop sur les Equations aux Dérivées Partielles Non Linéaires et Applications WEDP18

https://www.univ-setif.dz/OCS/WEDP2018/WEDP18
Citation

M. BENABDERRAHMANE Benyattou, (2018), "Deuxième Workshop sur les Equations aux Dérivées Partielles Non Linéaires et Applications WEDP18", [national] Deuxième Workshop sur les Equations aux Dérivées Partielles Non Linéaires et Applications WEDP18 , Sétif

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Comportement asymptotique pour un problème d'histoire viscoélastique dans le passé avec des conditions limites acoustiques

In this paper, we consider a viscoelastic equation of variable coefficients in the presence of infinite memory (past history) with nonlinear damping term and nonlinear delay term in the boundary feedback and acoustic boundary conditions. Under suitable assumptions, two arbitrary decay results of the energy solution are established via suitable Lyapunov functionals and some properties of the convex functions. The first stability result is given with a relation between the damping term and relaxation function and the second result is given without imposing any restrictive growth assumption on the damping term and the kernel function g. Our result extends the decay result obtained for problems with finite history to those with infinite history.
Citation

M. BENABDERRAHMANE Benyattou, (2018), "Comportement asymptotique pour un problème d'histoire viscoélastique dans le passé avec des conditions limites acoustiques", [national] Applicable Analysis , Taylor and Francis

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General decay for a viscoelastic equation of variable coefficients in the presence of past history with delay term in the boundary feedback and acoustic boundary conditions

In this paper, we consider a viscoelastic equation of variable coefficients in the presence of infinite memory (past history) with nonlinear damping term and nonlinear delay term in the boundary feedback and acoustic boundary conditions. Under suitable assumptions, two arbitrary decay results of the energy solution are established via suitable Lyapunov functionals and some properties of the convex functions. The first stability result is given with relation between the damping term and relaxation function. The second result is given without imposing any restrictive growth assumption on the damping term and the kernel function g. Our result extends the decay result obtained for problems with finite history to those with infinite history.
Citation

M. BENABDERRAHMANE Benyattou, Noukhatem Yamna, , (2018), "General decay for a viscoelastic equation of variable coefficients in the presence of past history with delay term in the boundary feedback and acoustic boundary conditions", [national] Acta Applicandae Mathematicae , Springer

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2017

On the asymptotic behavior of solutions for p-Laplacian type wave equations.

https://ntmsci.com/Conferences/ICAAMM2017
Citation

M. BENABDERRAHMANE Benyattou, (2017), "On the asymptotic behavior of solutions for p-Laplacian type wave equations.", [international] International Congress on Applied Analysis and Mathematical Modling, ICAAMM2017 , Istanbul-Turkey.

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Analysis of a quasistatic total slipdependent frictional contact problem for viscoelastic materials with long-term memory

In this paper, we study a mathematical problem modeling the antiplane shear deformation between a deformable cylinder body and a rigid foundation. We
assume that the behavior of the cylinder is described by a viscoelastic constitutive law with long-term memory. The contact is bilateral and the friction is modeled with Trasca's
friction law in which the friction bound depending on the total slip. We present the classical formulation of the antiplane problem and we derive the corresponding variational
formulation as a history slip-dependent evolutionary quasi-variational inequality with a Volterra integral term . Based on arguments of evolutionary variational inequalities with
viscosity and Banach's fixed point theorem, an existence and uniqueness result of the weak solution is proved. Furthermore, the behavior of the solution with respect to perturbations
of relaxation coefficients of long-term memory is considered and a convergence result is also given.
Citation

M. BENABDERRAHMANE Benyattou, (2017), "Analysis of a quasistatic total slipdependent frictional contact problem for viscoelastic materials with long-term memory", [national] Analele Universitatii Oradea. Fasc. Matematica , Universitatii Oradea

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2015

A nonlinear hyperbolic problem for viscoelastic equations

this paper, we consider a nonlinear boundary value problem for viscoelastic équations with a source term. By basing on Faedo-Galerkin approximations and compactness
argument, this work is devoted to prove thé existence, uniqueness, and aiso continuous dependence with respect to thé initial data of solutions.
Citation

M. BENABDERRAHMANE Benyattou, Rahmoune Abita, , (2015), "A nonlinear hyperbolic problem for viscoelastic equations", [national] Palestine Journal of Mathematics , Palestine Polytechnic University,

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2012

Multiplicative Schwarz method for nonlinear quasi-variational inequalities and their application in contact mechanics

In this paper, we present and analyze subspace correction method for the solution of nonlinear
quasi-variational inequalities and apply this theoretical result to non smooth contact
problems in nonlinear elasticity with slip-rate dependent friction. We introduce this method
in a Hilbert space, prove that it is globally convergent and give error estimates. In the context
of nite element discretization, where my method turns out to be one-and two-level Schwarz
methods, we specify their convergence rate and its dependence on the discretization parameters
and conclude that our methods converge optimally. Transferring this results to frictional
contact problems, we thus can overcome the mesh dependence of some xed-point schemas
which are commonly employed for contact problems with slip-rate dependent coecient of
Tresca and Coulomb friction.
Citation

M. BENABDERRAHMANE Benyattou, (2012), "Multiplicative Schwarz method for nonlinear quasi-variational inequalities and their application in contact mechanics", [international] 21th International Conference on Domain Decomposition Methods, DD21 , Rennes, France

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2011

Study of an Ill-Posed Boundary Value Problem in Contact Mechanics

B. Nouiri, B. Benabderrahmane, Study of an Ill-Posed Boundary Value Problem in Contact
Mechanics. The Third Conference on Mathematical Sciences, CMS'2011, Zarkaa private University
April 27-29, 2011, Jordan.
Citation

M. BENABDERRAHMANE Benyattou, (2011), "Study of an Ill-Posed Boundary Value Problem in Contact Mechanics", [international] The Third Conference on Mathematical Sciences, CMS'2011 , Zarkaa private University, Jordan.

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2010

Faedo-Galerkin method for a non linear boundary value problem associated to the elasticity equations

B. Benabderrahmane, B. Nouiri, A. Rahmoune, Faedo-Galerkin method for a non linear boundary
value problem associated to the elasticity equations, Fourth Saudi Science Conference,
March 21 - 24, 2010, Al-Madinah Al-Munawwarah, KSA.
Citation

M. BENABDERRAHMANE Benyattou, (2010), "Faedo-Galerkin method for a non linear boundary value problem associated to the elasticity equations", [international] Fourth Saudi Science Conference , Al-Madinah Al-Munawwarah, KSA

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Theoretical study for the quasi-static problem with dry friction for linear elastic materials and solid body

B. Nouiri, B. Benabderrahmane, Theoretical study for the quasi-static problem with dry friction
for linear elastic materials and solid body, Fourth Saudi Science Conference, March 21 - 24,
2010, Al-Madinah Al-Munawwarah, KSA.
Citation

M. BENABDERRAHMANE Benyattou, (2010), "Theoretical study for the quasi-static problem with dry friction for linear elastic materials and solid body", [international] Fourth Saudi Science Conference , Al-Madinah Al-Munawwarah, KSA

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2009

Relative Fredholm alternative to boundary value problem for the elliptic equations

B.Benabderrahmane and B. Nouiri, Relative Fredholm alternative to boundary value problem for the elliptic equations, Journal of Concrete And Applicable Mathematics, (JCAAM), Vol.7,
no.1, (2009) 82-94.
Citation

M. BENABDERRAHMANE Benyattou, (2009), "Relative Fredholm alternative to boundary value problem for the elliptic equations", [national] Journal of Concrete And Applicable Mathematics, (JCAAM) , University of Memphis

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Newmark method applied to the Elasto-dynamic problem with slip-rate dependent friction

B. Nouiri and B. Benabderrahmane, Newmark method applied to the Elasto-dynamic problem with slip-rate dependent friction, Journal of Concrete And Applicable Mathematics, (JCAAM),
Vol.7, no.1, (2009) 70-81.
Citation

M. BENABDERRAHMANE Benyattou, (2009), "Newmark method applied to the Elasto-dynamic problem with slip-rate dependent friction", [national] Journal of Concrete And Applicable Mathematics, (JCAAM) , University of Memphis

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A Quasistatic contact problem with slip dependent friction for linear elastic materials

B. Nouiri and B. Benabderrahmane, A Quasistatic contact problem with slip dependent friction
for linear elastic materials, International Conference of Mathematical Sciences, 04-10 August
2009, Istanbul, Turkey.
Citation

M. BENABDERRAHMANE Benyattou, (2009), "A Quasistatic contact problem with slip dependent friction for linear elastic materials", [international] International Conference of Mathematical Sciences , Istanbul, Turkey

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2008

Resolvent of the Lamé system in a polygone

B. Benabderrahmane, B., Nouiri, B., Resolvent of the Lamé system in a polygone, Anal. Univ. Oradea, fasc. Matematica, Tom XV (2008) 219-238.
Citation

M. BENABDERRAHMANE Benyattou, (2008), "Resolvent of the Lamé system in a polygone", [national] Anal. Univ. Oradea, fasc. Matematica , Univ. Oradea

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Singularity of a boundary value problem of the elasticity equations in a polyhedron

B. Benabderrahmane and B. Nouiri, Singularity of a boundary value problem of the elasticity equations in a polyhedron, Creat. Math. Inform., 17 (2008), No.2, 47-55.
Citation

M. BENABDERRAHMANE Benyattou, (2008), "Singularity of a boundary value problem of the elasticity equations in a polyhedron", [national] Creat. Math. Inform , North University Center at Baia Mare

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Index of the elasticity operator with contact without friction boundary

B. Benabderrahmane, B. Nouiri and Y. Boukhatem, Index of the elasticity operator with contact without friction boundary, Studia Univ. Babes-Bolyai, Mathematica, Vol. LIII, No.3, (2008) 3-11.
Citation

M. BENABDERRAHMANE Benyattou, (2008), "Index of the elasticity operator with contact without friction boundary", [national] Studia Univ. Babes-Bolyai, Mathematica , Univ. Babes-Bolyai

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Elasto-dynamic problem with friction depending on the speed of the slip

Nouiri, B., B. Benabderrahmane, B., Elasto-dynamic problem with friction depending on the speed of the slip, Anal. Univ. Oradea, fasc. Math., Tom XV (2008), 11-22.
Citation

M. BENABDERRAHMANE Benyattou, (2008), "Elasto-dynamic problem with friction depending on the speed of the slip", [national] Anal. Univ. Oradea, fasc. Math. , Univ. Oradea

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Singularity of the boundary value problem for the elliptic equations

B. Benabderrahmane and B. Nouiri, Singularity of the boundary value problem for the elliptic
equations, The Second Conference on Mathematical Sciences, CMS'2008, Zarkaa private
University October 22-23, 2008, Jordan.
Citation

M. BENABDERRAHMANE Benyattou, (2008), "Singularity of the boundary value problem for the elliptic equations", [international] The Second Conference on Mathematical Sciences, CMS'2008 , Zarkaa private University, Jordan.

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2007

Variational study of non linear problem of contact without friction between two Elastic bodies

B. Benabderrahmane and B. Nouiri, Variational study of non linear problem of contact without
friction between two Elastic bodies, International ISAAC Congress, 13 - 18 August 2007.
Ankara, Turkey.
Citation

M. BENABDERRAHMANE Benyattou, (2007), "Variational study of non linear problem of contact without friction between two Elastic bodies", [international] International ISAAC Congress , Ankara, Turkey

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Problem of contact without friction between two Elastic bodies

B. Benabderrahmane and B. Nouiri, Problem of contact without friction between two Elastic
bodies, The Second International Conference on Mathematics : Trends and Developments, 27th
to 30th December 2007 (ICMTD 2007), Cairo, Egypt.
Citation

M. BENABDERRAHMANE Benyattou, (2007), "Problem of contact without friction between two Elastic bodies", [national] The Second International Conference on Mathematics : Trends and Developments , Cairo, Egypt

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2006

Regularity Solutions for contact problem without friction of Elasticity's equations,

B.Benabderrahmane and B. Nouiri, Regularity Solutions for contact problem without friction of Elasticity's equations, Far East Journal of Applied Mathematics, Vol. 24, (2006), No. 3, 373-380.
Citation

M. BENABDERRAHMANE Benyattou, (2006), "Regularity Solutions for contact problem without friction of Elasticity's equations,", [national] Far East Journal of Applied Mathematics , University of Allahabad

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2005

Problème élasto-dynamique de frottement sec

B. Nouiri et B. Benabderrahmane. Problème élasto-dynamique de frottement sec. 5me Rencontre
Internationale sur l'analyse mathématiques et ses applications, RAMA5, 10, 11 et 12
Avril 2006, M'sila, Algérie.
Citation

M. BENABDERRAHMANE Benyattou, (2005), "Problème élasto-dynamique de frottement sec", [international] 5me Rencontre Internationale sur l'analyse mathématiques et ses applications, RAMA5 , M'sila, Algérie

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Problème de contact sans frottement entre deux corps déformables

B. Benabderrahmane et B. Nouiri, Problème de contact sans frottement entre deux corps déformables,
5me Rencontre Internationale sur l'analyse mathématiques et ses applications,RAMA5,
10, 11 et 12 Avril 2006, M'sila, Algérie.
Citation

M. BENABDERRAHMANE Benyattou, (2005), "Problème de contact sans frottement entre deux corps déformables", [international] 5me Rencontre Internationale sur l'analyse mathématiques et ses applications,RAMA5 , M'sila, Algérie

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