| Issue |
ESAIM: COCV
Volume 19, Number 2, April-June 2013
|
|
|---|---|---|
| Page(s) | 460 - 485 | |
| DOI | https://doi.org/10.1051/cocv/2012017 | |
| Published online | 15 February 2013 | |
Time optimal control of the heat equation with pointwise control constraints*,**
1
Institut für Mathematik, Karl-Franzens-Universität
Graz, A-8010
Graz,
Austria
karl.kunisch@uni-graz.at
2 School of Mathematics and Statistics,
Wuhan University, Wuhan
430072, P.R.
China
ljwang.math@whu.edu.cn
∗ Corresponding author.
Received:
6
September
2011
Revised:
6
February
2012
Time optimal control problems for an internally controlled heat equation with pointwise control constraints are studied. By Pontryagin’s maximum principle and properties of nontrivial solutions of the heat equation, we derive a bang-bang property for time optimal control. Using the bang-bang property and establishing certain connections between time and norm optimal control problems for the heat equation, necessary and sufficient conditions for the optimal time and the optimal control are obtained.
Mathematics Subject Classification: 35K05 / 49J20 / 49J30
Key words: Bang-bang property / time optimal control / norm optimal control
© EDP Sciences, SMAI, 2013
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