Controllability of a quantum particle in a moving potential well

By Karine Beauchard, Jean-Michel Coron. 2006

174 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5aa3c4cd36e1743fe18dca9290c5f34915ba2b51

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In Control and Systems Engineering

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

On the controllability of the 1-D isentropic Euler equation (2007, methodology): “Coron in [14] in the context of finite-dimensional systems, and used since for various PDE problems such as Euler incompressible equation [15, 19], Burgers equation [24], Vlasov–Poisson equation [20], Schrödinger equation [6, 7].”
Controllability of the discrete-spectrum Schrödinger equation driven by an external field (2008, background): “In [12, 13] Beauchard and Coron study the controllability of a quantum particle in a 1D potential well with W (x) = x.”
Control of a Korteweg-de Vries equation: A tutorial (2013, methodology): “To address this problem and the previous one, a possible approach would be to prove the exact controllability of the nonlinear equation around nontrivial stationary solutions (as proved by Crépeau in [20, 21] in the case of homogeneous Dirichlet boundary conditions), and then to apply the method int”
Local controllability of 1D linear and nonlinear Schr (2010, unknown): “Des résultats similaires ont déjá été établis (Beauchard, 2005, 2008, 2006) [14,15,17], mais dans des espaces non optimaux, en temps long et leur démonstration reposait sur le théorème de Nash–Moser, pour gérer une apparente perte de régularité.”
Boundary controllability for the nonlinear Korteweg–de Vries equation on any critical domain (2009, methodology): “For example, in [2] Beauchard and Coron proved, for a time large enough, the local exact controllability along the ground state trajectory of a Schrödinger equation and Coron proved in [9] and [10, Theorem 9.”
Exact boundary controllability of the nonlinear Schrödinger equation (2009, unknown): “v(x, 0) = v 0(x), (1.10) where ϕ ∈ C ∞(Rn, [0, 1 ]) satisfies”
GLOBAL STEADY-STATE STABILIZATION AND CONTROLLABILITY OF 1D SEMILINEAR WAVE EQUATIONS (2006, methodology): “The method consisting in stabilizing a quasi-static deformation has already been used in [8] in the context of nonlinear heat equations, in [23] for Navier–Stokes equations, in [7] for shallow water equations, and in [3, 4] for a Schrödinger equation.”