Coupled linear Schrödinger equations: Control and stabilization results

0585946 - MÚ 2025 RIV DE eng J - Článek v odborném periodiku
Bhandari, Kuntal - Capistrano-Filho, R. de A. - Majumdar, S. - Tanaka, T. Y.
Coupled linear Schrödinger equations: Control and stabilization results.
Zeitschrift für angewandte Mathematik und Physik. Roč. 75, č. 3 (2024), č. článku 97. ISSN 0044-2275. E-ISSN 1420-9039
Grant CEP: GA ČR(CZ) GC22-08633J
Institucionální podpora: RVO:67985840
Klíčová slova: boundary control * Carleman estimates * coupled Schrödinger equations
Obor OECD: Pure mathematics
Impakt faktor: 2, rok: 2022
Způsob publikování: Omezený přístup
https://doi.org/10.1007/s00033-024-02242-7

This article presents some controllability and stabilization results for a system of two coupled linear Schrödinger equations in the one-dimensional case where the state components are interacting through the Kirchhoff boundary conditions. Considering the system in a bounded domain, the null boundary controllability result is shown. The result is achieved thanks to a new Carleman estimate, which ensures a boundary observation. Additionally, this boundary observation together with some trace estimates, helps us to use the Gramian approach, with a suitable choice of feedback law, to prove that the system under consideration decays exponentially to zero at least as fast as the function e-2ωt for some ω>0.
Trvalý link: https://hdl.handle.net/11104/0353580