On the existence of time optimal controls for linear evolution equations

Kim Dang Phung; Gengsheng Wang; Xu Zhang

doi:10.3934/dcdsb.2007.8.925

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2007, Volume 8, Issue 4: 925-941. Doi: 10.3934/dcdsb.2007.8.925

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On the existence of time optimal controls for linear evolution equations

1.
Yangtze Center of Mathematics, Sichuan University, Chengdu 610064
2.
School of Mathematics and Statistics, Wuhan University, Wuhan 430072
3.
Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100190

Received: November 2006

Revised: May 2007

Published: November 2007

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Abstract

This work concerns with the existence of the time optimal controls for some linear evolution equations without the a priori assumption on the existence of admissible controls. Both global and local existence results are presented. Some necessary conditions, sufficient conditions, and necessary and sufficient conditions for the existence of time optimal controls are derived by establishing the relationship between controllability and time optimal control problems.

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Mathematics Subject Classification: Primary: 49J20; Secondary: 93B05, 35B37.

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