Salah ZITOUNI - Academia.edu (original) (raw)

Papers by Salah ZITOUNI

Research paper thumbnail of Well-posedness and general energy decay of solutions for a nonlinear damping piezoelectric beams system with thermal and magnetic effects

Hacettepe Journal of Mathematics and Statistics

In this article, we study the piezoelectric beams with thermal and magnetic effects in the presen... more In this article, we study the piezoelectric beams with thermal and magnetic effects in the presence of a nonlinear damping term acting on the mechanical equation. First, we prove that the system is well-posed in the sense of semigroup theory. And by constructing a suitable Liapunov functional, we show a general decay result of the solution for the system from which the polynomial and exponential decay are only special cases. Furthermore, our result does not depend on any relationship between system parameters.

Research paper thumbnail of Polynomial stability of Timoshenko system with strong damping and strong distributed delay terms

Research Square (Research Square), Nov 14, 2023

Research paper thumbnail of Existence and exponential stability of solutions for transmission system with varying delay in R

Mathematica Moravica, 2016

In the present paper we are going to consider in a one dimension bounded domain a transmission sy... more In the present paper we are going to consider in a one dimension bounded domain a transmission system with a varying delay. Under suitable assumptions on the weights of the damping and the delay terms, we prove the well-possedness and the uniqueness of solution using the semigroup theory. Also we show the exponential stability by introducing an appropriate Lyaponov functional.

Research paper thumbnail of Global Well-Posedness and Exponential Decay of Shear Beam Model Subject to a Neutral Delay

Eurasian Journal of Mathematical and Computer Applications

In this paper, we consider a one-dimensional system known as Shear beam model (no rotary inertia)... more In this paper, we consider a one-dimensional system known as Shear beam model (no rotary inertia) where the transverse displacement equation is subject to a distributed delay of neutral type. Under some assumptions on the kernel h, we first achieved the global well- posedness of the system by using the classical Faedo-Galerkin approximations along with two a priori estimates. Next, we find the energy expression and by using technique of Lyapunov functional we demonstrate, although delays are known to be of a destructive nature in the general case, that this system is exponentially stable regardless any relationship between coefficients of the system.

Research paper thumbnail of Global well-posedness and exponential decay of fully dynamic and electrostatic or quasi-static piezoelectric beams subject to a neutral delay

Zeitschrift für angewandte Mathematik und Physik

Research paper thumbnail of Exponential stability for a flexible structure with Fourier's type heat conduction and distributed delay

Differential Equations & Applications

In this paper, we study the well-posedness and asymptotic behaviour of solutions to a flexible st... more In this paper, we study the well-posedness and asymptotic behaviour of solutions to a flexible structure with Fourier's type heat conduction and distributed delay. We prove the wellposedness by using the semigroup theory. Also we establish a decay result by introducing a suitable Lyaponov functional.

Research paper thumbnail of Exponential stability to a laminated beam in thermoelasticity of type III with delay

Malaya Journal of Matematik

In this paper, we study the well-posedness and asymptotic behaviour of solutions to a laminated b... more In this paper, we study the well-posedness and asymptotic behaviour of solutions to a laminated beam in thermoelasticity of type III with delay term in the fourth equation. We first give the well-posedness of the system by using semigroup method and Lumer-Philips theorem. Then, by using the perturbed energy method and construct some Lyapunov functionals, we obtain the exponential decay result for the case of equal wave speeds.

Research paper thumbnail of General stability for piezoelectric beams with a nonlinear damping term

ANNALI DELL'UNIVERSITA' DI FERRARA

Research paper thumbnail of Well-posedness and general decay for a porous-elastic system with microtemperatures effects and time-varying delay term

Zeitschrift für angewandte Mathematik und Physik

Research paper thumbnail of Delayed flexible structure - Existence, uniqueness and exponential stability

In this paper, we concerned with a delayed flexible structure system, where the heat flux is give... more In this paper, we concerned with a delayed flexible structure system, where the heat flux is given by Cattaneo's law. We prove the wellposed of the system as well as its exponential stability under suitable hypotheses on the weights of the delay, heating effect and material damping.

Research paper thumbnail of Existence and Ulam stability results for two orders neutral fractional differential equations

Research paper thumbnail of Exponential decay and numerical solution of nonlinear Bresse-Timoshenko system with second sound

Journal of Thermal Stresses, 2022

Abstract This paper aims to study the one-dimensional nonlinear Bresse-Timoshenko system with sec... more Abstract This paper aims to study the one-dimensional nonlinear Bresse-Timoshenko system with second sound where the heat conduction given by Cattaneo’s law is effective in the second equation. We prove that the system is exponentially stable by using the energy method that requires constructing a suitable Lyapunov functional through exploiting the multipliers method. Furthermore, the result does not depend on any condition on the coefficients of the system. Finally, we validate our theoretical result by performing some numerical approximations based on the standard finite elements method, by using the backward Euler scheme for the temporal and spatial discretization.

Research paper thumbnail of Existence and Ulam stability for two orders delay fractional differential equations

Rendiconti di Matematica e delle sue Applicazioni. Serie VII, 2019

In this paper, we study the existence and uniqueness for nonlinear delay fractional differential ... more In this paper, we study the existence and uniqueness for nonlinear delay fractional differential equations with two orders of Caputo's fractional derivative using the Banach fixed point theorem. Also, we establish the Ulam stability of solutions. Finally, we give an example to illustrate the results.

Research paper thumbnail of Local existence and Ulam stability results for nonlinear fractional differential equations

Journal of Applied Nonlinear Dynamics, 2020

Research paper thumbnail of Well-posedness and decay of solutions to Bresse system with internal distributed delay

International journal of applied mathematics and statistics, 2017

We pursue the investigation started in a recent paper by (A. S. Nicaise and C. Pignotti, 2008) an... more We pursue the investigation started in a recent paper by (A. S. Nicaise and C. Pignotti, 2008) and later by (T. A. Apalara, 2014) concerning the wave equations driven by distributed delay term. Under more restrictive conditions on the weight of the distributed delay terms in the feedbacks, we prove the global existence of solutions for a one-dimensional linear Bresse system with internal distributed delay situated the first equation by means of semigroup theory in Sobolev spaces . Furthermore, we study the asymptotic behavior of solutions using the well known multiplier method.

Research paper thumbnail of Stability result for a nonlinear damping porous-elastic system with delay term

Nonlinear Studies, 2020

In this paper, we considered a one dimensional porous-elastic system with a delay term and nonlin... more In this paper, we considered a one dimensional porous-elastic system with a delay term and nonlinear damping term. We estabilished the well-posedness via the semi group theory and we showed the general decay of the solution for the case of equal speed of wave propagation in the two equations of the system.

Research paper thumbnail of General decay for a viscoelastic damped Timoshenko system of second sound with distributed delay

Journal | MESA, 2019

In this paper we consider a thermo-viscoelastic system of Timoshenko-type with nonlinear damping ... more In this paper we consider a thermo-viscoelastic system of Timoshenko-type with nonlinear damping and a distributed delay acting on transverse displacement. The heat flux of the system is governed by Cattaneo's law. We use the energy method and some properties of convex functions to prove, regardless of the speeds of wave propagation, general decay estimate from which the exponential, logarithmic and polynomial types of decay are only special cases.

Research paper thumbnail of Well-posedness and decay of solution for a transmission problem in the presence of infinite history and varying delay

Nonlinear Studies, 2018

In this article we consider a transmission problem in a bounded domain with a varying delay term ... more In this article we consider a transmission problem in a bounded domain with a varying delay term and the presence of infinite history in the first equation. Under suitable assumptions on the weight of the damping and the weight of the delay, we prove the existence and the uniqueness of the solution using the semigroup theory. Also we show the exponential stability of the solution by introducing a suitable Lyaponov functional.

Research paper thumbnail of Existence and stability of solution for transmission system with varying delay

International journal of applied mathematics and statistics, 2016

In this paper, under suitable assumptions on the weights of the damping and the delay terms, we p... more In this paper, under suitable assumptions on the weights of the damping and the delay terms, we prove the existence and uniqueness of solution for a coupled system of wave equations with a varying delay using the semi group theory in bounded domain. Also we show the stability result by introducing an appropriate Lyaponov functional.

Research paper thumbnail of Exponential decay for a thermo-viscoelastic Bresse system with second sound and delay terms

In this paper, we consider a thermo-viscoelastic Bresse system with second sound and delay terms,... more In this paper, we consider a thermo-viscoelastic Bresse system with second sound and delay terms, where the heat flux is given by Cattaneo’s law. Regardless of the speeds of wave propagation and the stable number, which is introduced in [14, 15], we prove an exponential stability result using energy method under suitable assumptions on the weights of the delays and the frictionals damping.

Research paper thumbnail of Well-posedness and general energy decay of solutions for a nonlinear damping piezoelectric beams system with thermal and magnetic effects

Hacettepe Journal of Mathematics and Statistics

In this article, we study the piezoelectric beams with thermal and magnetic effects in the presen... more In this article, we study the piezoelectric beams with thermal and magnetic effects in the presence of a nonlinear damping term acting on the mechanical equation. First, we prove that the system is well-posed in the sense of semigroup theory. And by constructing a suitable Liapunov functional, we show a general decay result of the solution for the system from which the polynomial and exponential decay are only special cases. Furthermore, our result does not depend on any relationship between system parameters.

Research paper thumbnail of Polynomial stability of Timoshenko system with strong damping and strong distributed delay terms

Research Square (Research Square), Nov 14, 2023

Research paper thumbnail of Existence and exponential stability of solutions for transmission system with varying delay in R

Mathematica Moravica, 2016

In the present paper we are going to consider in a one dimension bounded domain a transmission sy... more In the present paper we are going to consider in a one dimension bounded domain a transmission system with a varying delay. Under suitable assumptions on the weights of the damping and the delay terms, we prove the well-possedness and the uniqueness of solution using the semigroup theory. Also we show the exponential stability by introducing an appropriate Lyaponov functional.

Research paper thumbnail of Global Well-Posedness and Exponential Decay of Shear Beam Model Subject to a Neutral Delay

Eurasian Journal of Mathematical and Computer Applications

In this paper, we consider a one-dimensional system known as Shear beam model (no rotary inertia)... more In this paper, we consider a one-dimensional system known as Shear beam model (no rotary inertia) where the transverse displacement equation is subject to a distributed delay of neutral type. Under some assumptions on the kernel h, we first achieved the global well- posedness of the system by using the classical Faedo-Galerkin approximations along with two a priori estimates. Next, we find the energy expression and by using technique of Lyapunov functional we demonstrate, although delays are known to be of a destructive nature in the general case, that this system is exponentially stable regardless any relationship between coefficients of the system.

Research paper thumbnail of Global well-posedness and exponential decay of fully dynamic and electrostatic or quasi-static piezoelectric beams subject to a neutral delay

Zeitschrift für angewandte Mathematik und Physik

Research paper thumbnail of Exponential stability for a flexible structure with Fourier's type heat conduction and distributed delay

Differential Equations & Applications

In this paper, we study the well-posedness and asymptotic behaviour of solutions to a flexible st... more In this paper, we study the well-posedness and asymptotic behaviour of solutions to a flexible structure with Fourier's type heat conduction and distributed delay. We prove the wellposedness by using the semigroup theory. Also we establish a decay result by introducing a suitable Lyaponov functional.

Research paper thumbnail of Exponential stability to a laminated beam in thermoelasticity of type III with delay

Malaya Journal of Matematik

In this paper, we study the well-posedness and asymptotic behaviour of solutions to a laminated b... more In this paper, we study the well-posedness and asymptotic behaviour of solutions to a laminated beam in thermoelasticity of type III with delay term in the fourth equation. We first give the well-posedness of the system by using semigroup method and Lumer-Philips theorem. Then, by using the perturbed energy method and construct some Lyapunov functionals, we obtain the exponential decay result for the case of equal wave speeds.

Research paper thumbnail of General stability for piezoelectric beams with a nonlinear damping term

ANNALI DELL'UNIVERSITA' DI FERRARA

Research paper thumbnail of Well-posedness and general decay for a porous-elastic system with microtemperatures effects and time-varying delay term

Zeitschrift für angewandte Mathematik und Physik

Research paper thumbnail of Delayed flexible structure - Existence, uniqueness and exponential stability

In this paper, we concerned with a delayed flexible structure system, where the heat flux is give... more In this paper, we concerned with a delayed flexible structure system, where the heat flux is given by Cattaneo's law. We prove the wellposed of the system as well as its exponential stability under suitable hypotheses on the weights of the delay, heating effect and material damping.

Research paper thumbnail of Existence and Ulam stability results for two orders neutral fractional differential equations

Research paper thumbnail of Exponential decay and numerical solution of nonlinear Bresse-Timoshenko system with second sound

Journal of Thermal Stresses, 2022

Abstract This paper aims to study the one-dimensional nonlinear Bresse-Timoshenko system with sec... more Abstract This paper aims to study the one-dimensional nonlinear Bresse-Timoshenko system with second sound where the heat conduction given by Cattaneo’s law is effective in the second equation. We prove that the system is exponentially stable by using the energy method that requires constructing a suitable Lyapunov functional through exploiting the multipliers method. Furthermore, the result does not depend on any condition on the coefficients of the system. Finally, we validate our theoretical result by performing some numerical approximations based on the standard finite elements method, by using the backward Euler scheme for the temporal and spatial discretization.

Research paper thumbnail of Existence and Ulam stability for two orders delay fractional differential equations

Rendiconti di Matematica e delle sue Applicazioni. Serie VII, 2019

In this paper, we study the existence and uniqueness for nonlinear delay fractional differential ... more In this paper, we study the existence and uniqueness for nonlinear delay fractional differential equations with two orders of Caputo's fractional derivative using the Banach fixed point theorem. Also, we establish the Ulam stability of solutions. Finally, we give an example to illustrate the results.

Research paper thumbnail of Local existence and Ulam stability results for nonlinear fractional differential equations

Journal of Applied Nonlinear Dynamics, 2020

Research paper thumbnail of Well-posedness and decay of solutions to Bresse system with internal distributed delay

International journal of applied mathematics and statistics, 2017

We pursue the investigation started in a recent paper by (A. S. Nicaise and C. Pignotti, 2008) an... more We pursue the investigation started in a recent paper by (A. S. Nicaise and C. Pignotti, 2008) and later by (T. A. Apalara, 2014) concerning the wave equations driven by distributed delay term. Under more restrictive conditions on the weight of the distributed delay terms in the feedbacks, we prove the global existence of solutions for a one-dimensional linear Bresse system with internal distributed delay situated the first equation by means of semigroup theory in Sobolev spaces . Furthermore, we study the asymptotic behavior of solutions using the well known multiplier method.

Research paper thumbnail of Stability result for a nonlinear damping porous-elastic system with delay term

Nonlinear Studies, 2020

In this paper, we considered a one dimensional porous-elastic system with a delay term and nonlin... more In this paper, we considered a one dimensional porous-elastic system with a delay term and nonlinear damping term. We estabilished the well-posedness via the semi group theory and we showed the general decay of the solution for the case of equal speed of wave propagation in the two equations of the system.

Research paper thumbnail of General decay for a viscoelastic damped Timoshenko system of second sound with distributed delay

Journal | MESA, 2019

In this paper we consider a thermo-viscoelastic system of Timoshenko-type with nonlinear damping ... more In this paper we consider a thermo-viscoelastic system of Timoshenko-type with nonlinear damping and a distributed delay acting on transverse displacement. The heat flux of the system is governed by Cattaneo's law. We use the energy method and some properties of convex functions to prove, regardless of the speeds of wave propagation, general decay estimate from which the exponential, logarithmic and polynomial types of decay are only special cases.

Research paper thumbnail of Well-posedness and decay of solution for a transmission problem in the presence of infinite history and varying delay

Nonlinear Studies, 2018

In this article we consider a transmission problem in a bounded domain with a varying delay term ... more In this article we consider a transmission problem in a bounded domain with a varying delay term and the presence of infinite history in the first equation. Under suitable assumptions on the weight of the damping and the weight of the delay, we prove the existence and the uniqueness of the solution using the semigroup theory. Also we show the exponential stability of the solution by introducing a suitable Lyaponov functional.

Research paper thumbnail of Existence and stability of solution for transmission system with varying delay

International journal of applied mathematics and statistics, 2016

In this paper, under suitable assumptions on the weights of the damping and the delay terms, we p... more In this paper, under suitable assumptions on the weights of the damping and the delay terms, we prove the existence and uniqueness of solution for a coupled system of wave equations with a varying delay using the semi group theory in bounded domain. Also we show the stability result by introducing an appropriate Lyaponov functional.

Research paper thumbnail of Exponential decay for a thermo-viscoelastic Bresse system with second sound and delay terms

In this paper, we consider a thermo-viscoelastic Bresse system with second sound and delay terms,... more In this paper, we consider a thermo-viscoelastic Bresse system with second sound and delay terms, where the heat flux is given by Cattaneo’s law. Regardless of the speeds of wave propagation and the stable number, which is introduced in [14, 15], we prove an exponential stability result using energy method under suitable assumptions on the weights of the delays and the frictionals damping.