Boundary control of the Maxwell dynamical system: lack of controllability by topological reasons

¹ Saint-Petersburg Department of Steklov Mathematical Institute, Fontanka 27, Saint-Petersburg 191011, Russia; belishev@bel.pdmi.ras.ru. Supported by RFBR, grant 98-01-00314.
² Saint-Petersburg State University, Saint-Petersburg, Russia. Supported by RFBR, grant 99-01-00107.

Received: 11 June 1999
Revised: 30 December 1999

Abstract

The paper deals with a boundary control problem for the Maxwell dynamical system in a bounbed domain Ω ⊂ R³. Let Ω^T ⊂ Ω be the subdomain filled by waves at the moment T, T_* the moment at which the waves fill the whole of Ω. The following effect occurs: for small enough T the system is approximately controllable in Ω^T whereas for larger T < T_* a lack of controllability is possible. The subspace of unreachable states is of finite dimension determined by topological characteristics of Ω^T.