# Ouchenane DjamelUniversité Amar Telidji Laghouat · Department of Mathematics and Computer Science

Ouchenane Djamel

PHD, April 07, 2016. Annaba University, Algeria. HDR, March 19, 2019. Annaba University, Algeria.

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70

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Introduction

Dr. Djamel Ouchenane and his common name is Yacine was born in D. Azzaba, W. Skikda-Algeria. He received his PhD degree in mathematics on April 7, 2016 and the highest academic degree (HDR) specializing Functional analysis for the Applied mathematics on March 19, 2019 both from University of Annaba, Algeria. He research interests include: Stability and Blow up for hyperbolic system of PDE, Numerical Methods for PDEs, Mathematical Analysis of PDEs.

**Skills and Expertise**

## Publications

Publications (70)

The main goal of this paper is to investigate the exponential stability of the Timoshenko system in thermoelasticity of second sound with a time-varying delay term in the internal feedback. The well-posedness of the problem is assured by using the variable norm technique of Kato. Furthermore the stability of the system is shown by applying the ener...

In this manuscript, the behavior of a Herschel-Bulkley uid has been discussed in a thin layer in R 3 associated with a nonlinear stationary, nonisothermal, and incompressible model. Furthermore, the limit problem has been considered, and the studied problem in Ω ε is transformed into another problem de ned in Ω ε without the parameter Ω ε (ε is the...

In this paper we are investigating to figure out the exponential growth of solutions with L_{p}-norm of a viscoelastic Klein-Gordon wave equation with strong damping, source and delay terms.

In this work, a nonlinear viscoelastic wave equation is studied. By supposing distributed delay feedback acting on the boundary, we establish the general decay rate under suitable hypothesis.

In this article, we investigate a one-dimensional thermoelastic laminated beam system with nonlinear damping and viscoelastic dissipation on the effective rotation angle and through heat conduction in the interfacial slip equations. Under minimal conditions on the relaxation function and the relationship between the coefficients of the wave propaga...

This article concerns linear one-dimensional thermoelastic Timoshenko system with memory and distributed delay terms where the Cattaneo law governs the heat flux q ( x , t ) . We proved an exponential stability result by using the energy method combined with Lyapunov functional.

This work is concerned with a full von Kármán beam in the presence of infinite-memory, Microtemperature and distributed delay terms. Firstly we establish the well posedness of the system. Secondly, by considered the kernel h : R + → R + satisfying h(t) ≤ ξ(t)H(h(t)), ∀t ∈ R + , where ξ and H are functions satisfying some specific properties, and un...

As a continuity to the study by M. M. Al-Gharabli et al in [16], we consider a one-dimensional porous thermoelastic system with second sound, distributed delay term and nonlinear feedback. We show the well-posedness, using the semigroup theory, and establish an explicit and general decay rate result, using some properties of convex functions and th...

In this paper, we consider a mathematical model of a contact problem in thermo-electro-viscoelasticity. The body is in contact with an obstacle. The contact is frictional and bilateral with a moving rigid foundation which results in the wear of the contacting surface. We establish a variational formulation for the model and we prove the existence o...

In this paper, we consider the Cauchy problem of a third order in time nonlinear equation known as the Jordan-Moore-Gibson-Thompson (JMGT) equation with the presence of both memory. Using the well known energy method combined with Lyapunov functionals approach, we prove a general decay result, and we show a local existence result in appropriate fun...

We investigate in this work a singular one-dimensional viscoelastic system with a nonlinear source term, distributed delay, nonlocal boundary condition, and damping terms. By the theory of potential-well, the existence of a global solution is established, and by the energy method and the functional of Lyapunov, we prove the exponential decay result...

We introduce the concepts of Cohen positive strongly -summing and positive -dominated m-homogeneous polynomials. The version of Pietsch’s domination theorem for the first class among other results and a Bu-type theorem is proved, as well as some inclusions with other known spaces. Moreover, we present a characterization of these classes in tensor t...

A nonlinear viscoelastic wave equation with Balakrishnan-Taylor damping and distributed delay is studied. By the energy method we establish the general decay rate under suitable hypothesis.

In the present paper, we consider an important problem from the application perspective in science and engineering, namely, one-dimensional porous–elastic systems with nonlinear damping, infinite memory and distributed delay terms. A new minimal conditions, placed on the nonlinear term and the relationship between the weights of the different dampi...

Bresse-Timoshenko beam model with thermal, mass diffusion and thermoelastic effects is studied. We state and prove the well-posedness of problem. The global existence and uniqueness of the solution is proved by using the classical Faedo-Galerkin approximations along with two a priori estimates. We prove an exponential stability estimate for problem...

In this work, we consider a Bresse-Timoshenko type system of second sound with distributed delay term. Under suitable assumptions, we establish the global well-posedness of the initial and boundary value problem by using the Faedo-Galerkin approximations and some energy estimates. By using the energy method, we show exponential stability results fo...

In this paper we are investigating to …gure out the exponential growth of solutions with Lp-norm of a viscoelastic Klein-Gordon wave equation with strong damping, source and delay terms.

In the present paper, one-dimensional linear thermo-elastic system of Bresse type with past history and delay term is considered. We prove the well-posedness of problem using the semigroup method. By using the energy method, we discuss stability of the system for two cases. An exponential stability result of system (7) is obtained in the case where...

In this paper, the Timoshenko system with distributed delay term, fractional operator in the memory and spatial fractional thermal effect is considered, we will prove under some assumptions the global existence of a weak solution. Furthermore, we show some results about the stability of system by the semigroup method.

This work deals with the proof of local existence theorem of solutions for coupled nonlocal singular viscoelastic system with respect to the nonlinearity of source terms by using the Faedo–Galerkin method together with energy methods. This work makes a new contribution, since most of the previous works did not address the proof of the theorem of th...

As a continuity to the study by M. Kafini [24], we consider a logarithmic nonlinear wave condition with delay term. We obtain a blow-up result of solutions under suitable conditions.

The swelling porous thermoelastic system with the presence of temperatures, microtemperature effect, and distributed delay terms is considered. We will establish the well posedness of the system, and we prove the exponential stability result.
1. Introduction and Preliminaries
Eringen was the first to present a theory in which a mixture of viscous...

In this paper, we consider a nonlinear viscoelastic Kirchhoff equation with the presence of both distributed delay term, Balakrishnan-Taylor damping, and logarithmic nonlinearity. We describe a exponential decay of solutions, and we obtained the asymptotic stability result of the global solution. This study is a continuation of Boulaaras's works (M...

This manuscript deals with the existence and uniqueness for the fourth order of Moore-Gibson-Thompson equation with, source terms, viscoelastic memory and integral condition by using Galerkin's method.

We consider a one-dimensional linear thermoelastic Bresse system with delay term, forcing, and infinity history acting on the shear angle displacement. Under an appropriate assumption between the weight of the delay and the weight of the damping, we prove the well-posedness of the problem using the semigroup method, where an asymptotic stability re...

In this paper, we consider a coupled flexible structure system with distributed delay in two equations. We first give the well-posedness of the system by using a semigroup method. Then, by using the perturbed energy method and constructing some Lyapunov functionals, we obtain the exponential decay result.

This paper deals with the existence and uniqueness of solutions of a new class of Moore-Gibson-Thompson equation with respect to the nonlocal mixed boundary value problem, source term, and nonnegative memory kernel. Galerkin’s method was the main used tool for proving our result. This work is a generalization of recent homogenous work.
1. Introduc...

In this work, we consider a new full von Kármán beam model with thermal and mass diffusion effects according to the Gurtin-Pinkin model combined with time-varying delay. Heat and mass exchange with the environment during thermodiffusion in the von Kármán beam. We establish the well-posedness and the exponential stability of the system by the energy...

The paper deals with a one-dimensional porous-elastic system with thermoelasticity of type III and distributed delay term. This model is dealing with dynamics of engineering structures and nonclassical problems of mathematical physics. We establish the well posedness of the system, and by the energy method combined with Lyapunov functions, we discu...

In this paper, we consider a coupled Lame system with the presence of distributed delay term, viscoelastic, and logarithmic source terms. We describe an exponential decay of solutions, where an asymptotic stability result of global solution is obtained. This study is an extension to Boulaaras' work in Applicable Analysis (2019), 1–19.

In the present article, we consider a porous thermoelastic system with distributed delay term in second sound, by using the energy method combined with multiplicative technique, we show the polynomial decay estimate of (1.1) with (1.3) in Theorem 2.7 and exponential stability of (1.1) with conditions (3.1) in Theorem 3.4. A new restriction on delay...

This paper studies the system of coupled nondegenerate viscoelastic Kirchhoff equations with a distributed delay. By using the energy method and Faedo-Galerkin method, we prove the global existence of solutions. Furthermore, we prove the exponential stability result.

In this paper, we consider a swelling porous elastic system with a viscoelastic damping and distributed delay terms in the second equation. The coupling gives new contributions to the theory associated with asymptotic behaviors of swelling porous elastic soils. The general decay result is established by the multiplier method.
1. Introduction and P...

Algerian Journal of Engineering, Architecture and Urbanism

Algerian Journal of Engineering, Architecture and Urbanism

In this current work, we are interested in a system of two singular one-dimensional nonlinear equations with a viscoelastic, general source and distributed delay terms. The existence of a global solution is established by the theory of potential well, and by using the energy method with the function of Lyapunov, we prove the general decay result of...

Our main concern in this paper, is to prove the the stability combined well-posedness results of solutions for a linear Timoshenko’s beam laminated with thermoplastic and past history together with distributed delay terms for the both cases nonequal and equal speeds of wave propagation. By using of some of the usual basic theorems and well known me...

Nonlinear Bresse-Timoshenko beam model with thermal, mass diffusion and theormoelastic effects is studied. We state and prove the well-posedness of problem. The global existence and uniqueness of solution is proved by using the classical Faedo-Galerkin approximations along with two a priori estimates. We prove an exponential stability estimate unde...

The propagation of elastic waves in a porous medium with the presence of two differents damping terms is a complex phenomenon occuring in many applications, especially when it comes with the distributed delay. In this paper, we consider a one-dimensional thermoelastic system of Timo-shenko type, with nonlinear damping, infinite memory and distribut...

In this work, we are concerned with a problem for a nonlinear viscoelastic wave equation with strong damping, source and delay terms, we proved a blow up result for the solution with negative initial energy under suitable conditions.

In this work, we consider a linear thermoelastic laminated timoshenko beam with distributed delay, where the heat conduction is given by cattaneoâs law. we establish the well posedness of the system. For stability results, we prove exponential and polynomial stabilities of the system for the cases of equal and nonequal speeds of wave propagation.

In this work, we are concerned with a problem for coupled nonlinear viscoelastic wave equation with distributed delay and strong damping and source terms, under suitable conditions we prove the blow up result of solutions.

This present work deals with the blow up of coupled Klein-Gordon system with
strong damping, distributed delay and source terms, under suitable
conditions.

In this work, we consider a one-dimensional Timoshenko system of thermoelasticity of type III with past history and distributive delay. It is known that an arbitrarily small delay may be the source of instability. We establish the stability of the system for the cases of equal and nonequal speeds of wave propagation respectively. Our results show t...

This manuscript is mainly focusing on a general stability of solution for one-dimensional Timoshenko system with infinite history and distributed delay term regardless also of the speeds of wave propagation. We prove our result by using the energy method combined with some properties of convex functions.

In this paper, we are concerned with the problem of a nonlinear viscoelastic wave equation with distributed delay, strong damping and source terms. We obtain a blow-up result of solutions under suitable conditions.

In this work, the exponential growth of solutions for a coupled nonlinear Klein-Gordon system with distributed delay, strong damping, and source terms is proved. Take into consideration some suitable assumptions.

In this work, we are concerned with a problem for a vis-coelastic wave equation with strong damping, nonlinear source and delay terms. We show the exponential growth of solutions with Lp-norm. i.e. lim t→∞ u p p → ∞. Mathematics Subject Classification (2010): 35L05, 35L20, 58G16, 93D20.

This work studies the blow-up result of the solution of a coupled nonlocal singular viscoelastic equation with general source and localized frictional damping terms under some suitable conditions. This work is a natural continuation of the previous recent articles by Boulaaras et al. (Appl. Anal., 2020, https://doi.

In this work, we are concerned with a problem for a viscoelastic wave equation with strong damping, nonlinear source and distributed delay terms. We show the exponential growth of solution with $L_{p}$-norm. i.e.
$\lim\limits_{t\rightarrow \infty}\Vert u\Vert_p^p \rightarrow \infty$.

In this work we substantiation that the positive intial-energy solution for coupled nonlinear Klein-Gordon equations with degenerate damping and source terms. We will prove, with positive initial energy, the global nonex-istence of solution by concavity method.

In this work, we are concerned with a problem of a logarithmic nonlinear wave equation with time-varying delay term. We established the local existence result and we proved a blow up result for the solution with negative initial energy under suitable conditions, This improves earlier results in the literature, for time-varying delay. References [1]...

In this paper, we consider a Bresse-Timoshenko type system with distributed delay term. Under suitable assumptions, we establish the global well-posedness of the initial and boundary value problem by using the Faedo-Galerkin approximations and some energy estimates. By using the energy method, we show two exponential stability results for the syste...

we consider a one-dimensional porous-elastic system with the presence of both memory and distributed delay terms in the second equation. Using the well known energy method combined with Lyapunov functionals appraoch, we prove a general decay result given in main Theorem .

In this paper, we consider a system of nonlinear viscoelastic wave equations with degenerate damping and source terms. We prove, with positive initial energy, the global nonexistence of solution by concavity method.

In this paper, we consider a coupled Lamé system of nonlinear viscoelastic equations with general source terms. Under some suitable conditions on the initial data and the relaxation functions, we prove an asymptotic stability result of global solution taking into account that the kernel is not necessarily decreasing. This work generalizes and impro...

In this paper we consider a one-dimensional linear thermoelastic system of Timoshenko type with distributed delay term. The heat conduction is given by Cattaneo's law. Under an appropriate assumption between the weight of the delay and the weight of the damping, we prove the exponential stability result will be shown without the usual assumption on...

The paper considered here is one-dimensional linear thermo-elastic Bresse system with a distributed delay term in the first equation. We prove the well-posedness and exponential stability result, this later will be shown without the usual assumption on the wave speeds. To achieve our goals, we make use of the semi-group method.

In this paper, a problem which arises in a class of coupled viscoelasticity system is considered. We obtain the decay rate of the energy, for certain class of relaxation functions not necessarily exponentially or polynomially decaying to zero.

In this paper we consider a on-dimensional linear thermoelastic system of Timoshenko type, where the heat ﬂux is given by Cattaneo’s law. We consider damping terms acting on the ﬁrst and the second equation and we establish a general decay estimate where the exponential and polynomial decay rates are only particular cases. We establish our result w...

In this paper we consider a on-dimensional linear thermoelastic system of Timoshenko type, where the heat ﬂux is given by Cattaneo’s law. We consider damping terms acting on the ﬁrst and the second equation and we establish a general decay estimate where the exponential and polynomial decay rates are only particular cases. We establish our result w...

This thesis is devoted to study blow up and asymptotic decay for some hyperbolic sys-
tems. The first part of the thesis is composed of two chapters. In chapter 1, we consider
a system of nonlinear wave equations with degenerate damping and strong nonlinear
source terms. We prove that the solution blows up in time. In the chapter 2, we con-
sider a...

In this paper, we consider a one-dimensional linear thermoelastic system of Timoshenko type with a delay term in the feedback. The heat conduction is given by Cattaneo's law. Under an appropriate assumption between the weight of the delay and the weight of the damping, we prove the well-posedness of the problem. Furthermore, an exponential stabilit...

The global existence and nonexistence of solutions for a system of nonlinear wave equations with degenerate damping and source terms supplemented with initial and Dirichlet boundary conditions was shown by Rammaha and Sakuntasathien in a bounded domain Ω ⊂ [TEX equation: {{\mathbb{R}}^n} ] , n = 1, 2, 3, in the case where the initial energy is nega...

Blow up of solutions to systems of nonlinear wave equations with degenerate damping and source terms supplemented with the initial and Dirichlet boundary conditions is shown in [M. A. Rammaha and S. Sakuntasathien, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 5, 2658–2683 (2010; Zbl 1190.35144)], in a bounded domain Ω⊂ℝ n ,...

## Projects

Project (1)

Well-posedness, stability and numerical results