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arXiv · 1208.1032

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

Isaías P. de Jesus·Silvano B. de Menezes
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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.

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Isaías P. de Jesus, Silvano B. de Menezes. 2012-08-05. On the Approximate Controllability of Stackelberg-Nash Strategies for Linear Heat Equations in $\mathbb{R}^N$ with Potentials. https://arxiv.org/abs/1208.1032

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