Time Optimal Controls of Semilinear Heat Equation with Switching Control
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This paper is concerned with the bang-bang property of time optimal controls, governed by a semilinear heat equation in a bounded domain with switching controls acting locally into two open subsets. The proofs rely on an observability estimate from a positive measurable set in time for the linear heat equation, and a Kakutani fixed point argument.
KeywordsTime optimal control Bang-bang property Semilinear heat equation Observability estimate from measurable sets Switching control
Mathematics Subject Classifications35K58 49J20 49J30 93B07
The authors would like to thank the anonymous referees for their extremely careful reading of a previous version of the paper and for their very valuable suggestions. This work was partially supported by the National Science Foundation of China under Grants 11371285 and 91130022.
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