28 citations · 59 across the 15 of their papers we have counts for
16 papers
Stability for the stochastic heat equation with multiplicative noise via finite-dimensional feedback
Víctor Hernández-Santamaría, Kévin Le Balc'h, Liliana Peralta
In this paper, we study the long-time behavior of a stochastic heat equation with a class of infinite-dimensional multiplicative noises and localized control. We first illustrate t…
Geometric condition for the observability of electromagnetic Schrödinger operators on
Kévin Le Balc'h, Jingrui Niu, Chenmin Sun
In this article we revisit the observability of the Schrödinger equation on the two-dimensional torus. In contrast to the Schrödinger operator with a purely electric potential, for…
Control of blow-up profiles for the mass-critical focusing nonlinear Schrödinger equation on bounded domains
Ludovick Gagnon, Kévin Le Balc'h
In this paper, we consider the mass-critical focusing nonlinear Schrödinger on bounded two-dimensional domains with Dirichlet boundary conditions. In the absence of control, it is…
The Graph Geometric Control Condition
Kaïs Ammari, Alessandro Duca, Romain Joly +1
In this paper, we introduce a novel concept called the Graph Geometric Control Condition (GGCC). It turns out to be a simple, geometric rewriting of many of the frameworks in which…
The Kalman rank condition and the optimal cost for the null-controllability of coupled Stokes systems
Kévin Le Balc'h, Luz de Teresa
This paper considers the controllability of a class of coupled Stokes systems with distributed controls. The coupling terms are of a different nature. The first coupling is through…
-estimates, local well-posedness and controllability for linear and semilinear backward SPDEs
Víctor Hernández-Santamaría, Kévin Le Balc'h, Liliana Peralta
In this paper, we study linear backward parabolic SPDEs in bounded domains and present new a priori estimates for their weak solutions. Inspired by the seminal work of Y. Hu, J. Ma…
Almost sharp local Bernstein estimates for Laplace eigenfunctions on compact Riemannian manifolds
Kévin Le Balc'h
We study local growth properties of Laplace eigenfunctions on compact Riemannian manifolds. Following the paradigm introduced by Donnelly and Fefferman in the late 1980s, an eigenf…
Global stabilization of the cubic defocusing nonlinear Schrödinger equation on the torus
Kévin Le Balc'h, Jérémy Martin
In this article, we prove the (uniform) global exponential stabilization of the cubic defocusing Schrödinger equation on the torus d-dimensional torus, for d=1, 2 or 3, with a line…
Observability estimates for the Schr{ö}dinger equation in the plane with periodic bounded potentials from measurable sets
Kévin Le Balc'H, Jérémy Martin
The goal of this article is to obtain observability estimates for Schr{ö}dinger equations in the plane R 2. More precisely, considering a 2Z 2-periodic potential V L $\inf…
Global null-controllability for stochastic semilinear parabolic equations
Víctor Hernández-Santamaría, Kévin Le Balc'h, Liliana Peralta
In this paper, we prove the small-time global null-controllability of forward (resp. backward) semilinear stochastic parabolic equations with globally Lipschitz nonlinearities in t…
Exponential bounds for gradient of solutions to linear elliptic and parabolic equations
Kévin Le Balc'h
In this paper, we prove global gradient estimates for solutions to linear elliptic and parabolic equations. For a sufficiently smooth bounded convex domain ,…
Approximate controllability of the linearized Boussinesq system in a two dimensional channel
Kévin Le Balc'h
In this paper, we prove an approximate controllability result for the linearized Boussinesq system around a fluid at rest, in a two dimensional channel, when the control acts only…
Null-controllability of linear parabolic-transport systems
Karine Beauchard, Armand Koenig, Kévin Le Balc'h
Over the past two decades, the controllability of several examples of parabolic-hyperbolic systems has been investigated. The present article is the beginning of an attempt to find…
Global null-controllability and nonnegative-controllability of slightly superlinear heat equations
Kévin Le Balc'H
We consider the semilinear heat equation posed on a smooth bounded domain of with Dirichlet or Neumann boundary conditions. The control input is a source term…
Local controllability of reaction-diffusion systems around nonnegative stationary states
Kévin Le Balc'H
We consider a nonlinear reaction-diffusion system posed on a smooth bounded domain of . This system models reversible chemical reactions. We act on t…
Null-Controllability of Two Species Reaction-Diffusion System with Nonlinear Coupling: A New Duality Method
Kévin Le Balc'H
We consider a nonlinear reaction-diffusion system posed on a smooth bounded domain$$Ω\ge). The control input is in the source term of only one equation.…