On null-controllability of the heat equation on infinite strips and control cost estimate

2018/09/28 by Egidi, Michela
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1809.10942

Abstract

We consider an infinite strip Ω_L=(0,2πL)^d-1×ℝ, d≥ 2, L>0, and study the control problem of the heat equation on Ω_L with Dirichlet or Neumann boundary conditions, and control set ω⊂Ω_L. We provide a sufficient and necessary condition for null-controllability in any positive time T>0, which is a geometric condition on the control set ω. This is referred to as "thickness with respect to Ω_L" and implies that the set ω cannot be concentrated in a particular region of Ω_L. We compare the thickness condition with a previously known necessity condition for null-controllability and give a control cost estimate which only shows dependence on the geometric parameters of ω and the time T.

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