Geodesic
An optimal time control problem for the one-dimensional, linear heat equation, in the presence of a scaling parameter
Benalia, Karim1 ; David, Claire2  ; Oukacha, Brahim1 
1 Laboratory of operational research and mathematical decision, Mouloud Mammeri University, Tizi-Ouzou, Algeria.
2 Laboratoire Jacques-Louis Lions, 4, place Jussieu 75005, Paris, France, Sorbonne University, UPMC Univ Paris 06 CNRS, UMR 7598, Paris France.
RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 4, pp. 1289-1299

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In this paper, we study the optimal time problem for the one-dimensional, linear heat equation, in the presence of a scaling parameter. To begin with, we build an exact solution. The dependence of this solution as regards the scaling parameter naturally opens the way to study the existence and uniqueness of an optimal time control. If, moreover, one assumes the L ∞ - null controllability, it enables to establish a bang-bang type property.

DOI : 10.1051/ro/2017006
Classification : 35K05
Keywords: Optimal time control problem, null controllability, bang-bang property, heat equation, Scaling parameter

Benalia, Karim 1 ; David, Claire 2 ; Oukacha, Brahim 1

1 Laboratory of operational research and mathematical decision, Mouloud Mammeri University, Tizi-Ouzou, Algeria.
2 Laboratoire Jacques-Louis Lions, 4, place Jussieu 75005, Paris, France, Sorbonne University, UPMC Univ Paris 06 CNRS, UMR 7598, Paris France. 
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     author = {Benalia, Karim and David, Claire and Oukacha, Brahim},
     title = {An optimal time control problem for the one-dimensional, linear heat equation, in the presence of a scaling parameter},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {1289--1299},
     publisher = {EDP-Sciences},
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     doi = {10.1051/ro/2017006},
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Benalia, Karim; David, Claire; Oukacha, Brahim. An optimal time control problem for the one-dimensional, linear heat equation, in the presence of a scaling parameter. RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 4, pp. 1289-1299. doi: 10.1051/ro/2017006

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