Controllability of the heat equation with a control acting on a measurable set

Abstract

The paper deals with the controllability of a heat equation. It is well-known that the heat equation y _t − Δ _y = uχ _E in (0, T)×Ω with homogeneous Dirichlet boundary conditions is null controllable for any T > 0 and any open nonempty subset E of Ω. In this note, the author studies the case that E is an arbitrary measurable set with positive measure.

Keywords

Heat equation / Measurable sets / Null controllability / Observability inequality

References

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