46 citations · 144 across the 25 of their papers we have counts for
28 papers
Two escape rates for negative eigenvalues of quantum graphs with a shrinking core
Gregory Berkolaiko, Denis Borisov, Marshall King +1
We study the negative spectrum of the Laplacian on a metric graph with general vertex matching conditions and with two length scales: a compact core whose edges have length of orde…
Semigroup decay for the wave equation with unbounded damping
Antonio Arnal, Borbala Gerhat, Julien Royer +1
We study the damped wave equation with a damping coefficient which is possibly singular and unbounded at infinity. In general, zero belongs to the spectrum of the corresponding gen…
A minimal mass blow-up solution on a nonlinear quantum star graph
François Genoud, Stefan Le Coz, Julien Royer
We construct a finite-time blow-up solution to the mass-critical focusing nonlinear Schrödinger equation on a metric star graph with an arbitrary number of edges. We show that all…
Null-controllability properties of the generalized two-dimensional Baouendi-Grushin equation with non-rectangular control sets
Jérémi Dardé, Armand Koenig, Julien Royer
We consider the null-controllability problem for the generalized Baouendi-Grushin equation on a rectangular domain. Sharp…
On Duclos-Exner's conjecture about waveguides in strong uniform magnetic fields
Enguerrand Bon-Lavigne, Loïc Le Treust, Nicolas Raymond +1
We consider the Dirichlet Laplacian with uniform magnetic field on a curved strip in two dimensions. We give a sufficient condition ensuring the existence of the discrete spectrum…
Spectrum of the wave equation with Dirac damping on a non-compact star graph
David Krejcirik, Julien Royer
We consider the wave equation on non-compact star graphs, subject to a distributional damping defined through a Robin-type vertex condition with complex coupling. It is shown that…
Energy decay for a system of Schr{ö}dinger equations in a wave guide
Radhia Ayechi, Ilhem Boukhris, Julien Royer
We prove exponential decay for a system of two Schr{ö}dinger equations in a wave guide, with coupling and damping at the boundary. This relies on the spectral analysis of the corre…
Low frequency asymptotics and local energy decay for the Schr{ö}dinger equation
Julien Royer
We prove low frequency resolvent estimates and local energy decay for the Schr{ö}dinger equation in an asymptotically Euclidean setting. More precisely, we go beyond the optimal es…
Spectrum of a non-selfadjoint quantum star graph
Gabriel Riviere, Julien Royer
We study the spectrum of a quantum star graph with a non-selfadjoint Robin condition at the central vertex. We first prove that, in the high frequency limit, the spectrum of the Ro…
Absence of embedded eigenvalues for translationally invariant magnetic Laplacians
Nicolas Raymond, Julien Royer
Translationnally invariant bidimensional magnetic Laplacians are considered. Using an improved version of the harmonic approximation, we establish the absence of point spectrum und…
Stability of Standing Waves for a Nonlinear Klein-Gordon Equation with Delta Potentials
Elek Csobo, François Genoud, Masahito Ohta +1
In this paper, we study local well-posedness and orbital stability of standing waves for a singularly perturbed one-dimensional nonlinear Klein-Gordon equation. We first establish…
Energy decay for the Klein-Gordon equation with highly oscillating damping
Julien Royer
We consider the free Klein-Gordon equation with periodic damping. We show on this simple model that if the usual geometric condition holds then the decay of the energy is uniform w…
Energy decay and diffusion phenomenon for the asymptotically periodic damped wave equation
Romain Joly, Julien Royer
We prove local and global energy decay for the asymptotically periodic damped wave equation on the Euclidean space. Since the behavior of high frequencies is already mostly underst…
Reduction of dimension as a consequence of norm-resolvent convergence and applications
David Krejcirik, Nicolas Raymond, Julien Royer +1
This paper is devoted to dimensional reductions via the norm resolvent convergence. We derive explicit bounds on the resolvent difference as well as spectral asymptotics. The effic…
Energy Decay in a Wave Guide with Dissipation at Infinity
Mohamed Malloug, Julien Royer
We prove local and global energy decay for the wave equation in a wave guide with damping at infinity. More precisely, the absorption index is assumed to converge slowly to a posit…
Non-accretive Schrödinger operators and exponential decay of their eigenfunctions
David Krejcirik, Nicolas Raymond, Julien Royer +1
We consider non-self-adjoint electromagnetic Schrödinger operators on arbitrary open sets with complex scalar potentials whose real part is not necessarily bounded from below. Unde…
Local Energy Decay and Diffusive Phenomenon in a Dissipative Wave Guide
Julien Royer
We prove the local energy decay for the wave equation in a wave guide with dissipation at the boundary. It appears that for large times the dissipated wave behaves like a solution…
On the Cauchy problem and the black solitons of a singularly perturbed Gross-Pitaevskii equation
Isabella Ianni, Stefan Le Coz, Julien Royer
We consider the one-dimensional Gross-Pitaevskii equation perturbed by a Dirac potential. Using a fine analysis of the properties of the linear propagator, we study the well-posedn…
Local decay for the damped wave equation in the energy space
Julien Royer
We improve a previous result about the local energy decay for the damped wave equation on R^d. The problem is governed by a Laplacian associated with a long range perturbation of t…
Local energy decay and smoothing effect for the damped Schr{ö}dinger equation
Moez Khenissi, Julien Royer
We prove the local energy decay and the smoothing effect for the damped Schr{ö}dinger equation on R^d. The self-adjoint part is a Laplacian associated to a long-range perturbation…
Mourre's method for a dissipative form perturbation
Julien Royer
We prove uniform resolvent estimates for an abstract operator given by a dissipative perturbation of a self-adjoint operator in the sense of forms. For this we adapt the commutator…
Exponential decay for the Schr{ö}dinger equation on a dissipative waveguide
Julien Royer
We prove exponential decay for the solution of the Schr{ö}dinger equation on a dissipative waveguide. The absorption is effective everywhere on the boundary but the geometric contr…
Sharp low frequency resolvent estimates on asymptotically conical manifolds
Jean-Marc Bouclet, Julien Royer
On a class of asymptotically conical manifolds, we prove two types of low frequency estimates for the resolvent of the Laplace-Beltrami operator. The first result is a uniform $ L^…
Local Energy Decay for the Damped Wave Equation
Jean-Marc Bouclet, Julien Royer
We prove local energy decay for the damped wave equation on R^d. The problem which we consider is given by a long range metric perturbation of the Euclidean Laplacian with a short…