arXiv subjects

Mohamed Balegh

Publications and source records attributed to Mohamed Balegh.

4 recordsLinked to original sources

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↗

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↗