Approximate Controllability of a Semilinear Heat Equation in $\Bbb R^N$

We prove the approximate controllability of the semilinear heat equation in ${\Bbb R}^N$. We introduce the weighted Sobolev spaces of Escobedo and Kavian and in that functional setting we adapt the technique introduced by Fabre, Puel, and Zuazua for the problem in bounded domains. That is, we first prove the approximate controllability of the linear equation and by a fixed-point method obtain the main result.