On the Approximate Controllability of Stackelberg-Nash Strategies for   Linear Heat Equations in $\mathbb{R}^N$ with Potentials
  In this paper we establish hierarchic control for the linear heat equation in $\re^N$ with potentials. Our strategy is inspired by the techniques developed by J.I. D\'iaz and J.-L. Lions \cite{DL}; however many new difficulties arise due to lack of compactness of Sobolev embeddings. We manage these adversities by employing similarity variables and weighted Sobolev spaces. 
Isa\'ias P. de Jesus and Silvano B. de Menezes
math.OC