Advantages for controls imposed in a proper subset

Details Advantages for controls imposed in a proper subset Advantages for controls imposed in a proper subset

2012-01-19

arxiv.org/abs/1201.3967v1

Mathematics

Optimization and Control

14 pages

Scientific paper

In this paper, we study time optimal control problems for heat equations on $\Omega\times \mathbb{R}^+$. Two properties under consideration are the existence and the bang-bang properties of time optimal controls. It is proved that those two properties hold when controls are imposed on some proper subsets of $\Omega$; while they do not stand when controls are active on the whole $\Omega$. Besides, a new property for eigenfunctions of $-\Delta$ with Dirichlet boundary condition is revealed.

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