### Abstract

We discuss a class of linear control problems in a Hilbert space setting. The aim is to show that these control problems fit in a particular class of evolutionary equations such that the discussion of well-posedness becomes easily accessible. Furthermore, we study the notion of conservativity. For this purpose we require additional regularity properties of the solution operator in order to allow point-wise evaluations of the solution. We exemplify our findings by a system with unbounded control and observation operators.

Original language | English |
---|---|

Title of host publication | Progress in Partial Differential Equations |

Subtitle of host publication | Asymptotic Profiles, Regularity and Well-Posedness |

Place of Publication | Heidelberg |

Publisher | Springer |

Pages | 261-286 |

Number of pages | 26 |

ISBN (Print) | 9783319001241 |

DOIs | |

Publication status | Published - 29 May 2013 |

### Publication series

Name | Springer Proceedings in Mathematics & Statistics |
---|---|

Publisher | Springer |

Volume | 44 |

ISSN (Print) | 2194-1009 |

### Keywords

- Hilbert space
- linear control systems
- evolutionary equations
- conservativity
- well-posedness

## Cite this

Picard, R., Trostorff, S., & Waurick, M. (2013). A note on a class of conservative, well-posed linear control systems. In

*Progress in Partial Differential Equations: Asymptotic Profiles, Regularity and Well-Posedness*(pp. 261-286). (Springer Proceedings in Mathematics & Statistics; Vol. 44). Springer. https://doi.org/10.1007/978-3-319-00125-8