Exact null internal controllability for the heat equation on unbounded convex domains

Barbu, Viorel

ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 1, pp. 222-235.

The linear parabolic equation $\frac{\partial y}{\partial t}-\frac{1}{2}\Delta y+F·\nabla y={\mathbb{1}}_{{𝒪}_0}u$ with Neumann boundary condition on a convex open domain $𝒪\subset {ℝ}^d$ with smooth boundary is exactly null controllable on each finite interval if ${𝒪}_0$ is an open subset of $𝒪$ which contains a suitable neighbourhood of the recession cone of $\overline{𝒪}$. Here, $F:{ℝ}^d\to {ℝ}^d$ is a bounded, $C^1$-continuous function, and $F=\nabla g$ where $g$ is convex and coercive.

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