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

Free access article

Issue		ESAIM: COCV Volume 5, 2000


Page(s)		207 - 217
DOI		10.1051/cocv:2000108

DOI: 10.1051/cocv:2000108

ESAIM: COCV, March 2000, Vol. 5, p. 207-217

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

Mikhail Belishev
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.

Aleksandr Glasman
Saint-Petersburg State University, Saint-Petersburg, Russia.
Supported by RFBR, grant 99-01-00107.

Received June 11, 1999. Revised December 30, 1999.

Abstract: The paper deals with a boundary control problem for the Maxwell dynamical system in a bounbed domain $\Omega \subset {\bf R^3}$ . Let $\Omega^T \subset \Omega$ be the subdomain filled by waves at the moment T, $T_{\ast}$ the moment at which the waves fill the whole of $\Omega$ . The following effect occurs: for small enough T the system is approximately controllable in $\Omega^T$ whereas for larger $T<T_{\ast}$ a lack of controllability is possible. The subspace of unreachable states is of finite dimension determined by topological characteristics of $\Omega^T$ .

Keywords and phrases: Maxwell's dynamical system, boundary control, unreachable states, topology of a domain.

AMS Subject Classification: 93B05, 35B37, 35Q60, 78A25, 93C20.

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