arXiv subjects

Zayd Hajjej

Publications and source records attributed to Zayd Hajjej.

8 recordsLinked to original sources

arXiv2026

Stability and blow-up for a suspension bridge plate model with fractional damping and memory

We investigate a suspension bridge model described by a nonlinear plate equation incorporating internal fractional damping and infinite memory effects. The system also includes a nonlinear source term that may induce instability. Using semigroup theory, we first establish the local well-posedness of solutions in an appropriate energy space. We then derive conditions ensuring global existence and exponential stability of solutions. In contrast, when the initial energy is negative, we prove that solutions blow up in finite time, revealing a threshold phenomenon governing the long-term dynamics of the system. To complement the analytical results, we construct a numerical approximation using Summation-By-Parts finite differences with Simultaneous Approximation Terms (SBP-SAT) for spatial discretization and a Newmark scheme for time integration. The scheme preserves the structural properties of the continuous energy framework. Numerical experiments illustrate the stability and blow-up regimes predicted by the theoretical analysis.

math.AP↗

arXiv2023

Well-Posedness and Polynomial energy decay rate of a transmission problem for Rayleigh beam model with heat conduction

In this paper, we investigate the stability of the transmission problem for Rayleigh beam model with heat conduction. First, we reformulate our system into an evolution equation and prove our problem's well-posedness. Next, we demonstrate the resolvent of the operator is compact in the energy space, then by using the general criteria of Arendt-Batty, we prove that the thermal dissipation is enough to stabilize our model. Finally, a polynomial energy decay rate has been obtained which depends on the mass densities and the moments of inertia of the Rayleigh beams.

math.AP↗

arXiv2023

Stabilization of weakly coupled viscoelastic Kirchhoff plate and wave equations

In this paper, we consider a weakly coupled system consisting of a viscoelastic Kirchhoff plate equation involving free boundary conditions and the viscoelastic wave equation with Dirichlet boundary conditions in a bounded domain. By assuming a more general type of relaxation functions, we establish explicit and general decay rate results, using the multiplier method and some properties of the convex functions.

math.AP↗

arXiv2023

Exponential Stability and exact controllability of a system of coupled wave equations by second order terms (via Laplacian) with only one non-smooth local damping

The purpose of this work is to investigate the exponential stability of a second order coupled wave equations by laplacian with one locally internal viscous damping. Firstly, using a unique continuation theorem combined with a Carleman estimate, we prove that our system is strongly stable without any geometric condition. Secondly, using a combination of the multiplier techniques and the frequency domain approach, we show that our system is exponentially stable under \textbf{(PMGC)} condition on the damping region without any restriction on wave propagation speed (i.e whether the two wave equations propagate at the same speed or not)

math.AP↗

arXiv2022

Stability and instability results of the Kirchhoff plate equation with delay terms on boundary or dynamical boundary controls

In this paper, we consider the Kirchhoff plate equation with delay terms on the boundary control are added (see system \eqref{p5-2.1} below). we give some instability examples of system \eqref{p5-2.1} for some choices of delays. Finally, we prove its well-posedness, strong stability without any geometric condition and exponential stability under a multiplier geometric control condition.

math.AP↗

arXiv2019

Uniform decay rates for a suspension bridge with locally distributed nonlinear damping

We study a nonlocal evolution equation modeling the deformation of a bridge, either a footbridge or a suspension bridge. Contrarily to the previous literature we prove the asymptotic stability of the considered model with a minimum amount of damping which represents less cost of material. The result is also numerically proved.

math.AP↗

arXiv2013

Uniformly exponentially stable approximations for a class of damped systems with unbounded feedbacks

In this paper we study time semi-discrete approximations of a class of exponentially stable infinite dimensional systems with unbounded feedbacks. It has recently been proved that for time semi-discrete systems, due to high frequency spurious components, the exponential decay property may be lost as the time step tends to zero. We prove that adding a suitable numerical viscosity term in the numerical scheme, one obtains approximations that are uniformly exponentially stable with respect to the discretization parameter

math.OC↗

arXiv2013

Uniformly polynomially stable approximations for a class of second order evolution equations

In this paper we study time semi-discrete approximations of a class of polynomially stable infinite dimensional systems modeling the damped vibrations. We prove that adding a suitable numerical viscosity term in the numerical scheme, one obtains approximations that are uniformly polynomially stable with respect to the discretization parameter.

math.OC↗