46 citations · 144 across the 25 of their papers we have counts for
15 papers · 1 filter
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 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…
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…
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…
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…
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…
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…
Semiclassical measure for the solution of the Helmholtz equation with an unbounded source
Julien Royer
We study the high frequency limit for the dissipative Helmholtz equation when the source term concentrates on a submanifold of R^n. We prove that the solution has a unique semi-cla…
Uniform resolvent estimates for a non-dissipative Helmholtz equation
Julien Royer
We study the high frequency limit for a non-dissipative Helmholtz equation. We first prove the absence of eigenvalue on the upper half-plane and close to an energy which satisfies…
Semiclassical measure for the solution of the dissipative Helmholtz equation
Julien Royer
We study the semiclassical measures for the solution of a dissipative Helmholtz equation with a source term concentrated on a bounded submanifold. The potential is not assumed to b…