41 citations · 69 across the 12 of their papers we have counts for
15 papers
Part II On strong and non uniform stability of locally damped Timoshenko beam: Mathematical corrections to the proof of Theorem 2.2 in the publication referenced as [1] in the bibliography
Fatiha Alabau-Boussouira
In part I of the rebuttal (see [2] to the article [1] entitled "Uniform stabilization for the Timoshenko beam by a locally distributed damping" published in 2003, in the journal El…
Part I: Rebuttal to "Uniform stabilization for the Timoshenko beam by a locally distributed damping"
Fatiha Alabau-Boussouira
A paper, entitled "Uniform stabilization for the Timoshenko beam by a locally distributed damping" was published in 2003, in the journal Electronic Journal of Differential Equation…
Bilinear control of evolution equations with unbounded lower order terms. Application to the Fokker-Planck equation
Fatiha Alabau-Boussouira, Piermarco Cannarsa, Cristina Urbani
We study the exact controllability of the evolution equation \begin{equation*} u'(t)+Au(t)+p(t)Bu(t)=0 \end{equation*} where is a nonnegative self-adjoint operator on a Hilbert…
Rebuttal to "Well-posedness and optimal decay rates for the viscoelastic Kirchhoff equation"
Fatiha Alabau-Boussouira
A paper, entitled "Well-posedness and optimal decay rates for the viscoelastic Kirchhoff equation" was published in 2016, in the journal Boletim da Sociedade Paranaense de Matemati…
Exact controllability to eigensolutions for evolution equations of parabolic type via bilinear control
Fatiha Alabau-Boussouira, Piermarco Cannarsa, Cristina Urbani
In a separable Hilbert space , we study the controlled evolution equation \begin{equation*} u'(t)+Au(t)+p(t)Bu(t)=0, \end{equation*} where () is a self-adjoin…
Superexponential stabilizability of evolution equations of parabolic type via bilinear control
Fatiha Alabau-Boussouira, Piermarco Cannarsa, Cristina Urbani
We prove rapid stabilizability to the ground state solution for a class of abstract parabolic equations of the form \begin{equation*} u'(t)+Au(t)+p(t)Bu(t)=0,\qquad t\geq0 \end{equ…
Nonlinear damped partial differential equations and their uniform discretizations
Fatiha Alabau-Boussouira, Yannick Privat, Emmanuel Trélat
We establish sharp energy decay rates for a large class of nonlinearly first-order damped systems, and we design discretization schemes that inherit of the same energy decay rates,…
Control and stabilization of degenerate wave equations
Fatiha Alabau-Boussouira, Piermarco Cannarsa, Günter Leugering
We study a wave equation in one space dimension with a general diffusion coefficient which degenerates on part of the boundary. Degeneracy is measured by a real parameter .…
A one-step optimal energy decay formula for indirectly nonlinearly damped hyperbolic systems coupled by velocities
Fatiha Alabau-Boussouira, Zhiqiang Wang, Lixin Yu
In this paper, we consider the energy decay of a damped hyperbolic system of wave-wave type which is coupled through the velocities. We are interested in the asymptotic properties…
Finite-time stabilization of a network of strings
Fatiha Alabau-Boussouira, Vincent Perrollaz, Lionel Rosier
We investigate the finite-time stabilization of a tree-shaped network of strings. Transparent boundary conditions are applied at all the external nodes. At any internal node, in ad…
Exponential stability of the wave equation with memory and time delay
Fatiha Alabau-Boussouira, Serge Nicaise, Cristina Pignotti
We study the asymptotic behaviour of the wave equation with viscoelastic damping in presence of a time-delayed damping. We prove exponential stability if the amplitude of the time…
Insensitizing exact controls for the scalar wave equation and exact controllability of -coupled cascade systems of PDE's by a single control
Fatiha Alabau-Boussouira
We study the exact controllability, by a reduced number of controls, of coupled cascade systems of PDE's and the existence of exact insensitizing controls for the scalar wave equat…
A hierarchic multi-level energy method for the control of bi-diagonal and mixed n-coupled cascade systems of PDE's by a reduced number of controls
Fatiha Alabau-Boussouira
This work is concerned with the exact controllability/observability of abstract cascade hyperbolic systems by a reduced number of controls/observations. We prove that the observati…
Controllability of cascade coupled systems of multi-dimensional evolution PDE's by a reduced number of controls
Fatiha Alabau-Boussouira
We prove controllability results for abstract systems of weakly coupled evolution equations in cascade by a reduced number of boundary or locally distributed controls ranging f…
Indirect stabilization of weakly coupled systems with hybrid boundary conditions
F. Alabau-Boussouira, P. Cannarsa, R. Guglielmi
We investigate stability properties of indirectly damped systems of evolution equations in Hilbert spaces, under new compatibility assumptions. We prove polynomial decay for the en…