15 citations · 22 across the 10 of their papers we have counts for
11 papers
Note on the Exponential Stability of the Viscoelastic Wave Equation
Ludovick Gagnon
In this article, we study the viscoelastic wave equation with a localized history memory term, and without frictional damping. Under the geometric control condition on the memory r…
DeepRitzSplit Neural Operator for Phase-Field Models via Energy Splitting
Chih-Kang Huang, Ludovick Gagnon, Miha Založnik +1
The multi-scale and non-linear nature of phase-field models of solidification requires fine spatial and temporal discretization, leading to long computation times. This could be ov…
Fredholm backstepping for critical operators and application to rapid stabilization for the linearized water waves
Ludovick Gagnon, Amaury Hayat, Shengquan Xiang +1
Fredholm-type backstepping transformation, introduced by Coron and Lü, has become a powerful tool for rapid stabilization with fast development over the last decade. Its strength l…
Fredholm transformation on Laplacian and rapid stabilization for the heat equation
Ludovick Gagnon, Amaury Hayat, Shengquan Xiang +1
We study the rapid stabilization of the heat equation on the 1-dimensional torus using the backstepping method with a Fredholm transformation. We prove that, under some assumption…
A Fredholm transformation for the rapid stabilization of a degenerate parabolic equation
Ludovick Gagnon, Pierre Lissy, Swann Marx
This paper deals with the rapid stabilization of a degenerate parabolic equation with a right Dirich-let control. Our strategy consists in applying a backstepping strategy, which s…
Control and exponential stability for a transmission problem of a viscoelastic wave equation
Remi Buffe, Marcelo Cavalcanti, Valéria Domingos Cavalcanti +1
In this article, we consider the energy decay of a viscoelastic wave in an heterogeneous medium. To be more specific, the medium is composed of two different homogeneous medium wit…
Sufficient Conditions for the Controllability of Wave Equations with a Transmission Condition at the Interface
Ludovick Gagnon
We consider waves travelling in two different mediums each endowed with a different constant speed of propagation. At the interface between the two mediums, the refraction of the r…
Recovering the uniform boundary observability with spectral Legendre-Galerkin formulations of the 1-D wave equation
Ludovick Gagnon, José Urquiza
For a Legendre-Galerkin semi-discretization of the 1-D homogeneous wave equation, the high frequency components of the numerical solution prevent us from obtaining the boundary obs…
Rapid Stabilization of a Linearized Bilinear Schrödinger Equation
Jean-Michel Coron, Ludovick Gagnon, Morgan Morancey
We consider the one dimensional Schrödinger equation with a bilinear control and prove the rapid stabilization of the linearized equation around the ground state. The feedback law…
Qualitative Description of the Particle Trajectories for the -Solitons Solution of the Korteweg-de Vries Equation
Ludovick Gagnon
The qualitative properties of the particle trajectories of the -solitons solution of the KdV equation are recovered from the first order velocity field by the introduction of th…
Lagrangian Controllability of the 1-D Korteweg-de Vries Equation
Ludovick Gagnon
We consider in this paper the problem of the Lagrangian controllability for the Korteweg-de Vries equation. Using the -solitons solution, we prove that, for any length of the sp…