The bang-bang property of time and norm optimal control problems for parabolic equations with time-varying fractional Laplacian
ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 7.

In this paper, we establish the bang-bang property of time and norm optimal control problems for parabolic equations governed by time-varying fractional Laplacian, evolved in a bounded domain of ℝ$$. We firstly get a quantitative unique continuation at one point in time for parabolic equations governed by time-varying fractional Laplacian. Then, we establish an observability inequality from measurable sets in time for solutions of the above-mentioned equations. Finally, with the aid of the observability inequality, the bang-bang property of time and norm optimal control problems can be obtained.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2017075
Mots-clés : Time optimal control, norm optimal control, bang-bang property, observability estimates, measurable sets, fractional Laplacian
Yu, Xin 1 ; Zhang, Liang 1

1 
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     title = {The bang-bang property of time and norm optimal control problems for parabolic equations with time-varying fractional {Laplacian}},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
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Yu, Xin; Zhang, Liang. The bang-bang property of time and norm optimal control problems for parabolic equations with time-varying fractional Laplacian. ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 7. doi : 10.1051/cocv/2017075. http://www.numdam.org/articles/10.1051/cocv/2017075/

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