On the Approximate Controllability of Stackelberg-Nash Strategies for Linear Heat Equations in ${\mathbb{R}}^N$ with Potentials

Abstract

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. Díaz 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.