Volume 51, Number 4, October-December 2017
|Page(s)||1289 - 1299|
|Published online||27 November 2017|
An optimal time control problem for the one-dimensional, linear heat equation, in the presence of a scaling parameter
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.
3 Laboratory of operational research and mathematical decision, Mouloud Mammeri University, Tizi-Ouzou, Algeria.
Received: 25 June 2016
Accepted: 6 January 2017
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.
Mathematics Subject Classification: 35K05
Key words: Optimal time control problem / null controllability / bang-bang property / heat equation / Scaling parameter
© EDP Sciences, ROADEF, SMAI 2017
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