Abstract
The aim of this work is to study the controllability of the Schrödinger equation i @t u(t) D -Åu(t) on Ω(t) with Dirichlet boundary conditions, where Ω(t) ⊂ RN is a time-varying domain. We prove the global approximate controllability of the equation in L2(Ω), via an adiabatic deformation Ω(t) ⊂ RN (t 2 Œ0; T ç) such that Ω(0) D Ω(T) D Ω. This control is strongly based on the Hamiltonian structure of the equation provided by Duca and Joly [Ann. Henri Poincaré 22 (2021), 2029–2063], which enables the use of adiabatic motions. We also discuss several explicit interesting controls that we perform in the specific framework of rectangular domains.
Original language | English |
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Pages (from-to) | 511-553 |
Number of pages | 43 |
Journal | Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire |
Volume | 41 |
Issue number | 3 |
DOIs | |
State | Published - 1 Jan 2024 |
Externally published | Yes |
Keywords
- Fermi acceleration
- PDEs on moving domains
- Schrödinger equation
- adiabatic control
- global approximate controllability
ASJC Scopus subject areas
- Analysis
- Mathematical Physics
- Applied Mathematics