10 papers
Blow-up for weakly superlinear heat equations and blow-up controllability of the linear heat equation
Kévin Le Balc'h, Philippe Souplet
The aim of this article is twofold: (a) to revisit the blow-up theory of weakly superlinear heat equations; (b) to explore the notion of internal global/regional blow-up controllab…
On the observability of the Schrödinger equation in the torus from open sets
Kévin Le Balc'h, Jiaqi Yu
We study the observability of the Schrödinger equation on the -dimensional torus , , from an open subset . Our first main result e…
Stability for the stochastic heat equation with multiplicative noise via finite-dimensional feedback
VÃctor Hernández-SantamarÃa, Kévin Le Balc'h, Liliana Peralta
In this paper, we study the long-time behavior of a stochastic heat equation with multiplicative noise and localized control. We begin by analyzing the uncontrolled dynamics and de…
-estimates, local well-posedness and controllability for linear and semilinear backward SPDEs
VÃctor Hernández-SantamarÃa, 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…
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…