Controllability of the Schrödinger equation on unbounded domains without geometric control condition

2022/06/21 by Matthias Täufer, Täufer, Matthias · 1 citation
Engineering · Mathematics · #35Q93 #93Bxx #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2206.10204

openalex publication_date 2022/06/21 · openalex created_date 2022/06/24 · openalex updated_date 2026/07/28

Abstract

We prove controllability of the Schrödinger equation in ℝ^d in any time T > 0 with internal control supported on nonempty, periodic, open sets. This demonstrates in particular that controllability of the Schrödinger equation in full space holds for a strictly larger class of control supports than for the wave equation and suggests that the control theory of Schrödinger equation in full space might be closer to the diffusive nature of the heat equation than to the ballistic nature of the wave equation. Our results are based on a combination of Floquet-Bloch theory with Ingham-type estimates on lacunary Fourier series.

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