### 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 T_{1} > 0 such that the system is approximately boundary controllable in any time T > 2T_{1}. It is also shown that there exists a time T_{2} < T_{1} such that the system is not boundary controllable in any time T < 2T_{2}. For a certain class of boundary controls, a necessary and sufficient condition for strict boundary controllability is obtained.

Original language | English |
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Pages (from-to) | 283-298 |

Number of pages | 16 |

Journal | IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications) |

Volume | 20 |

Issue number | 3 |

DOIs | |

Publication status | Published - Nov 1977 |

Externally published | Yes |