no. 2
Time optimal control of the heat equation with pointwise control constraints
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 2, pp. 460-485.

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.

DOI : 10.1051/cocv/2012017
Classification : 35K05, 49J20, 49J30
Mots clés : bang-bang property, time optimal control, norm optimal control 
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     title = {Time optimal control of the heat equation with pointwise control constraints},
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     publisher = {EDP-Sciences},
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Kunisch, Karl; Wang, Lijuan. Time optimal control of the heat equation with pointwise control constraints. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 2, pp. 460-485. doi : 10.1051/cocv/2012017. http://archive.numdam.org/articles/10.1051/cocv/2012017/

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