Zobrazeno 1 - 10
of 21
pro vyhledávání: '"Balc'h, Kevin Le"'
We consider the heat equation on a bounded $C^1$ domain in $\mathbb{R}^n$ with Dirichlet boundary conditions. The primary aim of this paper is to prove that the heat equation is observable from any measurable set with a Hausdorff dimension strictly g
Externí odkaz:
http://arxiv.org/abs/2407.20954
In this paper, we study linear backward parabolic SPDEs and present new a priori estimates for their weak solutions. Inspired by the seminal work of Y. Hu, J. Ma and J. Yong from 2002 on strong solutions, we establish $L^p$-estimates requiring minima
Externí odkaz:
http://arxiv.org/abs/2406.18500
Autor:
Balc'h, Kévin Le
This actual version contains a bad mistake, located in Section 2.3 that invalidates the proofs of the main results.
Comment: Comments are welcome
Comment: Comments are welcome
Externí odkaz:
http://arxiv.org/abs/2406.16036
Autor:
Balc'h, Kévin Le, Martin, Jérémy
In this paper, we investigate quantitative propagation of smallness properties for the Schr\"odinger operator on a bounded domain in $\mathbb R^d$. We extend Logunov, Malinnikova's results concerning propagation of smallness for $A$-harmonic function
Externí odkaz:
http://arxiv.org/abs/2403.15299
In this paper we investigate when linearly independent eigenfunctions of the Schr\''odinger operator may have the same modulus. General properties are established and the one-dimensional case is treated in full generality. The study is motivated by i
Externí odkaz:
http://arxiv.org/abs/2403.08341
Autor:
Balc'h, Kévin Le, Souza, Diego A.
In this article, we study a quantitative form of the Landis conjecture on exponential decay for real-valued solutions to second order elliptic equations with variable coefficients in the plane. In particular, we prove the following qualitative form o
Externí odkaz:
http://arxiv.org/abs/2401.00441
Autor:
Balc'h, Kévin Le, Martin, Jérémy
In this article, we prove the (uniform) global exponential stabilization of the cubic defocusing Schr\"odinger equation on the torus d-dimensional torus, for d=1, 2 or 3, with a linear damping localized in a subset of the torus satisfying some geomet
Externí odkaz:
http://arxiv.org/abs/2310.10805
Autor:
Balc'H, Kévin Le, Martin, Jérémy
The goal of this article is to obtain observability estimates for Schr{\"o}dinger equations in the plane R 2. More precisely, considering a 2$\pi$Z 2-periodic potential V $\in$ L $\infty$ (R 2), we prove that the evolution equation i$\partial$tu = --
Externí odkaz:
http://arxiv.org/abs/2304.08050
Autor:
Balc'h, Kévin Le, Takahashi, Takéo
In this paper, we consider a nonlinear system of two parabolic equations, with a distributed control in the first equation and an odd coupling term in the second one. We prove that the nonlinear system is small-time locally null-controllable. The mai
Externí odkaz:
http://arxiv.org/abs/2212.07647
In this paper, we prove the small-time global null-controllability of forward (resp. backward) semilinear stochastic parabolic equations with globally Lipschitz nonlinearities in the drift and diffusion terms (resp. in the drift term). In particular,
Externí odkaz:
http://arxiv.org/abs/2010.08854