Advantages for controls imposed in a proper subset

2012/01/19 by Wang, Gengsheng, Yashan Xu, Xu, Yashan
Computer Science · Engineering · Mathematics · #34H15 #49N20 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1201.3967

openalex publication_date 2012/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study time optimal control problems for heat equations on Ω× 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 Ω; while they do not stand when controls are active on the whole Ω. Besides, a new property for eigenfunctions of -Δ with Dirichlet boundary condition is revealed.

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