The Null Controllability of Transmission Wave-Schrödinger System with a Boundary Control

Ya Ping Guo*, Jun Min Wang, Jing Wang, Dong Xia Zhao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

This paper is devoted to investigate the null controllability of the transmission wave-Schrödinger system with only one boundary control. The domain of the system consists of two bounded intervals, where the wave and Schrödinger equations evolve, respectively. Two kinds of transmission conditions are considered: one is the simple continuous transmission, and by using the HUM method, the null controllability of the system is derived in the Hilbert space when a boundary control is added only on the wave equation. The other case is that the Schrödinger state is associated with the velocity of the wave, and we establish the null controllability of the system. It is found that the second space has more regularity.

Original languageEnglish
Article number27
JournalJournal of Dynamical and Control Systems
Volume30
Issue number3
DOIs
Publication statusPublished - Sept 2024

Keywords

  • Boundary control
  • Null controllability
  • Transmission system

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