77 citations · 222 across the 17 of their papers we have counts for
17 papers
Uniform stabilization of an acoustic system
Kaïs Ammari, Fathi Hassine, Luc Robbiano
We study the problem of stabilization for the acoustic system with a spatially distributed damping. With imposing hypothesis on the structural properties of the damping term, we id…
Semi-classical defect measure and internal stabilization for the semilinear wave equation subject to Zarembaboundary conditions
Marcelo Cavalcanti, Pierre Cornilleau, Valéria Domingos Cavalcanti +2
In this article we exploite the uniform decay for damped linear wave equation with Zaremba boundary condition, obtained in a previous work, to treat the same problem in nonlinear c…
Exponential stabilization of waves for the Zaremba boundary condition
Pierre Cornilleau, Luc Robbiano
In this article we prove, under some geometrical condition on geodesic flow, exponential stabilization of wave equation with Zaremba boundary condition. We prove an estimate on the…
Logarithmic stabilization of an acoustic system with a damping term of Brinkman type
Kaïs Ammari, Fathi Hassine, Luc Robbiano
We study the problem of stabilization for the acoustic system with a spatially distributed damping. Without imposing any hypotheses on the structural properties of the damping term…
Stabilization for vibrating plate with singular structural damping
Kaïs Ammari, Fathi Hassine, Luc Robbiano
We consider the dynamic elasticity equation, modeled by the Euler-Bernoulli plate equation, with a locally distributed singular structural (or viscoelastic ) damping in a boundary…
Stabilization of fractional-evolution systems
Kaïs Ammari, Fathi Hassine, Luc Robbiano
This paper is devoted to the analysis of the problem of stabilization of fractional (in time) partial differential equations. We consider the following equation $$ \partial^{α,η}_{…
Logarithmic Decay of a Wave Equation with Kelvin-Voigt Damping
Luc Robbiano, Qiong Zhang
In this paper we analyze the long time behavior of a wave equation with local Kelvin-Voigt Damping. Through introducing proper class symbol and pseudo-differential calculus, we obt…
Stability estimate in the inverse scattering for a single quantum particle in an external short-range potential
Luc Robbiano, Mourad Bellassoued
In this paper we consider the inverse scattering problem for the Schr{ö}dinger operator with short-range electric potential. We prove in dimension n 2 that the knowledge of…
Fractional-feedback stabilization for a class of evolution systems
Kaïs Ammari, Fathi Hassine, Luc Robbiano
We study the problem of stabilization for a class of evolution systems with fractional-damping. After writing the equations as an augmented system we prove in this article first th…
Comments on observability and stabilization of magnetic Schr{ö}dinger equations
Kaïs Ammari, Mourad Choulli, Luc Robbiano
We are mainly interested in extending the known results on ob-servability inequalities and stabilization for the Schr{ö}dinger equation to the magnetic Schr{ö}dinger equation. That…
Spectral inequality and resolvent estimate for the bi-Laplace operator
Jérôme Le Rousseau, Luc Robbiano
On a compact Riemannian manifold with boundary, we prove a spectral inequality for the bi-Laplace operator in the case of so-called "clamped" boundary conditions , that is, homogen…
Counting function for interior transmission eigenvalues
Luc Robbiano
In this paper we give results on the counting function associated with the interior transmission eigenvalues. For a complex refraction index we estimate of the counting function by…
Spectral analysis on interior transmission eigenvalues
Luc Robbiano
In this paper we prove some results on interior transmission eigenvalues. First, under rea- sonable assumptions, we prove that the spectrum is a discrete countable set and the gene…
The Kato Smoothing Effect for Regularized Schrödinger Equations in Exterior Domains
Lassaad Aloui, Moez Khenissi, Luc Robbiano
We prove, under the exterior geometric control condition, the Kato smoothing effect for solutions of an inhomogenous and damped Schrödinger equation on exterior domains.
Local well-posedness and blow up in the energy space for a class of L2 critical dispersion generalized Benjamin-Ono equations
Carlos E. Kenig, Yvan Martel, Luc Robbiano
We consider a family of dispersion generalized Benjamin-Ono equations (dgBO) which are critical with respect to the L2 norm and interpolate between the critical modified (BO) equat…
The Kato smoothing effect for Schr{ö}dinger equations with unbounded potentials in exterior domains
Luc Robbiano, Claude Zuily
In this paper we prove the smoothing effect for solutions of Schr{ö}dinger equations with variable coefficients and in a non trapping exterior domain. We allow quadratic potentials…
Remark on the Kato smoothing effect for Schrödinger equation with superquadratic potentials
Luc Robbiano, Claude Zuily
The aim of this note is to extend recent results of Yajima-Zhang \cite{Y-Z1, Y-Z2} on the 1/2- smoothing effect for Schrödinger equation with potential growing at infinity faster t…