Boundary controllability of linear symmetric hyperbolic systems

B. M N Clarke*

*Corresponding author for this work

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We consider the finite time boundary value controllability of a linear symmetric hyperbolic system subject to what will be known as "natural" boundary conditions. Such a system occurs frequently in mathematical physics and is, in a sense, the most general linear hyperbolic equation. It includes the equations of linear elasticity, electro-magnetic theory and acoustic wave motion. It will be shown that when the system differential operator satisfies a backward uniqueness property and is self adjoint, there exists a time T1 > 0 such that the system is approximately boundary controllable in any time T > 2T1. It is also shown that there exists a time T2 < T1 such that the system is not boundary controllable in any time T < 2T2. For a certain class of boundary controls, a necessary and sufficient condition for strict boundary controllability is obtained.

Original languageEnglish
Pages (from-to)283-298
Number of pages16
JournalIMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
Volume20
Issue number3
DOIs
Publication statusPublished - Nov 1977
Externally publishedYes

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