41 citations · 69 across the 12 of their papers we have counts for
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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…
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…
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…
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…