Time Optimal Controls of Semilinear Heat Equation with Switching Control

  • Lijuan Wang
  • Qishu Yan


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.


Time optimal control Bang-bang property Semilinear heat equation Observability estimate from measurable sets Switching control 

Mathematics Subject Classifications

35K58 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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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsWuhan UniversityWuhanChina

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