arXiv subjects

Abdelkader Saïdi

Publications and source records attributed to Abdelkader Saïdi.

4 recordsLinked to original sources

arXiv2014

The best decay rate of the damped plate equation in a square

In this paper we study the best decay rate of the solutions of a damped plate equation in a square and with a homogeneous Dirichlet boundary conditions. We show that the fastest decay rate is given by the supremum of the real part of the spectrum of the infinitesimal generator of the underlying semigroup, if the damping coefficient is in $L^\infty(Ω).$ Moreover, we give some numerical illustrations by spectral computation of the spectrum associated to the damped plate equation. The numerical results obtained for various cases of damping are in a good agreement with theoretical ones. Computation of the spectrum and energy of discrete solution of damped plate show that the best decay rate is given by spectral abscissa of numerical solution.

math.OC↗

arXiv2011

Theorical and Numerical Analysis of the Rapid Pointwise Stabilization of Coupled String-Beam Systems

We consider a pointwise stabilization problem for a coupled wave and plate equations. We prove under rather general assumptions, that such systems can stabilized so as to have arbitrarily high decay rates and are exactly controllable. We propose a numerical approximation of the model and we study numerically the construction of the feedbak law leading to exponential decay with arbtrarily large rate.

math.OC↗

arXiv2011

Homographic scheme for Riccati equation

In this paper we present a numerical scheme for the resolution of matrix Riccati equation, usualy used in control problems. The scheme is unconditionnaly stable and the solution is definite positive at each time step of the resolution. We prove the convergence in the scalar case and present several numerical experiments for classical test cases.

math.NA↗

arXiv2011

Unconditionnally stable scheme for Riccati equation

We present a numerical scheme for the resolution of matrix Riccati equation used in control problems. The scheme is unconditionnally stable and the solution is definite positive at each time step of the resolution. We prove the convergence in the scalar case and present several numerical experiments for classical test cases.

math.NA↗