The liner parabolic equation $\frac{y}{t}-\frac{1}{2}𝔻y+F·y={\overrightarrow{1}}_{{}_0}u$ ∂y ∂t − 1 2   Δy + F · ∇ y = 1 x1d4aa; 0 u with Neumann boundary condition on a convex open domain x1d4aa; ⊂ ℝd with smooth boundary is exactly null controllable on each finite interval if 𝒪0is an open subset of x1d4aa; which contains a suitable neighbourhood of the recession cone of $$ x1d4aa; . Here,F : ℝd → ℝd is a bounded, C1-continuous function, and F = ∇g, where g is convex and coercive.