EXACT NULL INTERNAL CONTROLLABILITY FOR THE HEAT EQUATION ON UNBOUNDED CONVEX DOMAINS

The liner parabolic equation partial derivative y/partial derivative t - 1/2 Delta y+F center dot del y = 1O(0) u with Neumann boundary condition on a convex open domain O subset of 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 (O) over bar. Here, F : R-d -> R-d is a bounded, C-1- continuous function, and F = del g, where g is convex and coercive.