Khemmoudj Ammar

• Professor (Full )
• Professor (Full) at University of Sciences and Technology Houari Boumediene

In this article, we consider a viscoelastic wave equation of Kirchhoff type in a bounded domain with a distributed delay term present in the nonlinear internal dambing. By introducing a functional energy and suitable Lyapunov functional, under suitable assumptions, we establish a general decay result from which the exponential and polynomial decay...

In this paper, we present a stability analysis of a piezoelectric beam subjected to either the Coleman-Gurtin or Gurtin-Pipkin thermal law, with added damping mechanisms in the x-and z-directions of the electric field. We demonstrate that controlling the electrical field components in these directions is unnecessary for achieving exponential decay...

We consider the stabilization of two weakly dissipative wave equations with variable coefficients, localized Kelvin–Voigt damping, mixed boundary condition and time delay. The well posedness is obtained by the semigroup method. Using a unique continuation result, we show that the system is strongly stable. Then, we show that the system is not expon...

In this paper, we are interested in designing a suitable boundary control to suppress axial vibration in a varying-length mining cable. The existence of a solution to the closed loop system is proved using the Faedo-Galerkin method. And by using Lyapunov’s method, we have shown that the closed-loop system with the boundary control is exponentially...

In this paper, we present an analysis of stability of solutions corresponding to a variable coefficient's wave equation subject to a locally Kelvin–Voigt damping and distributed effect driven by a nonnegative function b(x)≥0$$ b(x)\ge 0 $$ with dynamic Wentzell boundary conditions and delay term. By using frequency domain approach method, we show t...

In this paper, we present the analysis of stability for a piezoelectric beam subject to a thermal law (Coleman-Gurtin or Gurtin-Pipkin thermal law) adding some viscous damping mechanism to the electric field in $x-$direction and $z-$direction, and we discuss several cases. Then, there is no need to control the electrical field components in $x$-dir...

In this paper, we investigated the vibration control of a satellite with two symmetric flexible panels attached with center body. The panels are modeled as transmission Euler-Bernoulli beam. We have proved the well posedness by using semi group theory. By applying a control force at the center body of the spacecraft, we established exponential deca...

In this paper, we have analyzed the influence of viscoelastic and frictional damping on the decay rate of solutions for a Kirchhoff-type viscoelastic wave equation with a distributed delay acting on nonlinear internal damping. Taking the relaxation function of a fairly large class and using the method of energy in which we introduce an adapted Lyap...

In this paper we consider a nonlinear viscoelastic beam with a linear delay term and infinite memory term. The well posedness of solutions is proved using the semigroup method. We establish a general decay results by using minimal and general conditions on the relaxation function, from which the usual exponential and polynomial decay rates are only...

In this work, we study the existence and uniqueness of the solution to a wave equation with dynamic Wentztell-type boundary conditions on a part of the boundary Γ 1 of the domain Ω with non-linear delays in non-linear dampings in Ω and on Γ 1 , using the Faedo-Galerkin method.

In this paper, we consider a viscoelastic Petrovsky equation with localised nonlinear damping in bounded domain. The nonlinear damping is effective only in a neighborhood of a suitable subset of the boundary. Using the Faedo–Galerkin approximations together with some energy estimates, we prove the global existence of the solutions. Under the same a...

In a bounded domain, we consider the wave equation with localized Kelvin-Voigt damping and dynamic boundary conditions of Wentzell type with delay. First of all, using semi group theory we prove the existence and uniqueness of a solution in a suitable energy space. Secondly, by relying on Arendt-Batty’s criteria we prove the strong stability under...

An axially moving beam in a two-dimensional space is considered with nonlinear tension. A suitable boundary control is applied at the free end of the beam to suppress the undesirable vibration. The exponential stability result is proven by Lyapunov method.

The uniform stabilization of a semilinear wave equation with variable coefficients and nonlinear boundary conditions is considered. The uniform decay rate is established by the Riemannian geometry method.

In this study, we show that the solution of Timoshenko systems with past history and dynamical boundary condition decays polynomially in the case where the wave speeds of equations are different. Our method is based on the semigroup technique and the contraction argument of frequency domain method.

In this paper, the displacements in the transverse directions of the beam with memory term and bending couplings are considered. Under the lowest conditions on the kernel function the result of general decay is proven by multiplier method.

A longitudinal and transversal vibrations of the beam with nonlinear tension, a viscoelastic damping and distributed delay term is studied. Using the Faedo–Galerkin method, the well-posedness of the problem is established. A uniform decay result is proved by multiplier method.

We investigate the longitudinal and transversal vibrations of the viscoelastic beam with nonlinear tension and nonlinear delay term under the general decay rate for relaxation function. The existence theorem is proved by the Faedo–Galerkin method and using suitable Lyapunov functional to establish the general decay result.

In this paper we consider a multidimensional thermoviscoelastic system of Bresse type where the heat conduction is given by Green and Naghdi theories. For a wider class of relaxation functions, We show that the dissipation produced by the memory effect is strong enough to produce a general decay results. We establish a general decay results, from w...

In this paper, we examine a Bidirectional Associative Memory neural network model with distributed delays. Using a result due to Cid [J. Math. Anal. Appl. 281 (2003) 264–275], we were able to prove an exponential stability result in the case when the standard Lipschitz continuity condition is violated. Indeed, we deal with activation functions whic...

In this paper, we consider a wave equation with Wentzell dynamical boundary conditions and internal and boundary delay terms. We have obtained a global existence and energy decay estimates of the solutions to our problem for nonlinear dampings and nonlinear time delay terms. We would like to see the influence of frictional damping on the rate of de...

In this paper, we consider a viscoelastic Bresse-type system subjects to nonlinear damping, nonlinear time delay term, a finite memory and with homogeneous Dirichlet-Neumann-Neumann boundary conditions. Under a condition between the weight of delay term in the feedback and the weight of the term without delay, we prove, in case of equal speeds of w...

In this paper, we consider a viscoelastic rotating Euler-Bernoulli beam that has one end fixed to a rotated motor in a horizontal plane and to a tip mass at the other end. For a large class relaxation function q, namely, q'(t) ≤ −ζ(t)H(q(t)), where H is an increasing and convex function near the origin and ζ is a nonincreasing function, we establis...

In this paper we consider a viscoelastic modified nonlinear Von- Karman system with a linear delay term. The well posedness of solutions is proved using the Faedo-Galerkin method. We use minimal and general conditions on the relaxation function and establish a general decay results, from which the usual exponential and polynomial decay rates are on...

In this paper, vibration reduction of a viscoelastic flexible beam conveying fluid with variable velocity is studied. A control is designed at the top boundary of the beam based on original infinite dimensionality PDEs model and Lyapunov's direct method to reduce the beam's vibrations. The uniform stability under external disturbance and exponentia...

A viscoelastic beam in a two-dimensional space is considered with nonlinear tension. A boundary feedback is applied at the right boundary of the beam to suppress the undesirable vibration. The well-posedness of the problem is established. With the multiplier method, a uniform decay result is proven.

A viscoelastic beam in a two-dimensional space is considered with nonlinear tension. A boundary feedback is applied at the right boundary of the beam to suppress the undesirable vibration. The well-posedness of the problem is established. With the multiplier method, a uniform decay result is proven.

Background: King Hussein Cancer Foundation and Center (KHCF & KHCC) lead Breast Cancer (BC) awareness in Jordan through the Jordan Breast Cancer Program. The program aims to reduce morbidity and mortality from BC, and shift the current state of diagnosis from late stages to earlier ones, where the disease is curable, survival rates are higher, and...

In this article we consider a nonlinear viscoelastic Petrovsky equation in a bounded domain with distributed delay |ut (x, t)|lutt (x, t) + �2u(x, t) − �utt (x, t) − � t 0 h(t − σ)�2u(x, σ) dσ + μ1ut (x, t) + � τ2 τ1 μ2(s)ut (x, t − s)ds = 0, x ∈ �, t > 0, and prove a global solution existence result using the energy method combined with the Faedo–...

In this paper we study a viscoelastic nonlinear beam in two-dimensional space. We establish the well-posedness and a decay result. The proposed boundary controller guarantees that when there are no external forces, the beam is globally exponentially stabilized at its equilibrium position and that when the forces are presented, the beam is stabilize...

This paper is devoted to the study of uniform decay of a wave equation with dynamical boundary conditions, localised memory term and frictional dampings. We prove that a localised memory term combined with frictional dissipations is strong enough, via transmission process (u|Γ = v), to assure the asymptotic stability of the whole system.

In this paper we are concerned with a multi-dimensional Bresse system, in a bounded domain, where the memory-type damping is acting on a portion of the boundary. We establish a general decay results, from which the usual exponential and polynomial decay rates are only special cases.

In this paper we are concerned with a multi-dimensional Bresse system, in a bounded domain, where the memory-type damping is acting on a portion of the boundary. We establish a general decay results, from which the usual exponential and polynomial decay rates are only special cases.

In this paper, we study the stabilization of solutions of an axially moving string of kirchhoff type by a viscoelastic boundary control. We prove that the dissipation produced by the viscoelastic term is sufficient to suppress the transversal vibrations that occur during the axial motion of the string, and we also show that the string displacement...

In this paper, we consider a viscoelastic flexible structure modeled as an Euler-Bernoulli beam. The beam is moving in the direction of its axis. This is one of the main features of this work. We will be dealing with variable intervals of integration and therefore the standard computation using differentiation under the integral sign is no longer v...

In this paper, we consider a one-dimensional Bresse system with Cattaneo’s type heat conduction and a nonlinear weakly dissipative boundary feedback localized on a part of the boundary. We show the well-posedness, using the semigroup theory, and establish an explicit and general decay rate result without imposing a specific growth assumption on the...

In this paper, we are concerned with asymptotic stability of a class of Bresse-type system with three boundary dissipations. The beam has a rigid body attached to its free end. We show that exponential stabilization can be achieved by applying force and moment feedback boundary controls on the shear, longitudinal, and transverse displacement veloci...

In this paper, we study a cantilevered Euler-Bernoulli beam �xed to a base in a translational motion at one end and to a tip mass at its free end. The beam is subject to undesirable vibrations and it is made of a viscoelastic material which permits a certain weak damping. By applying a control force at the base we shall attenuate these vibrations i...

In this paper, we study the stabilization of a semi-linear viscoelastic wave equation subject to semi-linear and dynamical boundary conditions. The kernels used are of strongly positive definite type. We prove that internal and boundary memory damping are strong enough, via transmission process (u|Γ=v), to stabilize the whole system.

In this paper, we prove an exponential decay result for the energy associated to a flexible marine riser with vessel dynamics. By applying a control at the top boundary of the riser we shall attenuate its vibration in a fast manner. The method is based on the multiplier technique. The riser is modeled as a viscoelastic beam with a (slightly perturb...

In this paper, we are concerned with asymptotic stability of a class of Bresse-type system with three boundary dissipations. The beam has a rigid body attached to its free end. We show that exponential stabilization can be achieved by applying force and moment feedback boundary controls on the shear, longitudinal, and transverse displacement veloci...

In this paper, the uniform stabilization of the Cauchy–Ventcel problem with variable coefficients is considered, and the uniform energy decay rate for the problem is established by Riemannian geometry methods.

Le but de ce travail est d’ étudier la décroissance exponentielle del’énergie des solutions losque le temps tend vers l’infini du problème aux limites de Cauchy-Ventcel semi-linéaire dissipatif dans un domaine borné. On donne des conditions suffisantes sur les non linéarités de f et g pour avoir la décroissance exponentielle de l’énergie. Ce problème...