46 citations · 144 across the 25 of their papers we have counts for
8 papers · 1 filter
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…
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…
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…
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…
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^…
Limiting absorption principle for the dissipative Helmholtz equation
Julien Royer
Adapting Mourre's commutator method to the dissipative setting, we prove a limiting absorption principle for a class of abstract dissipative operators. A consequence is the resolve…