Abstract
In this paper, we establish hierarchic control for the linear heat equation in ℝN with potentials. Our strategy is inspired by the techniques developed by Díaz and Lions [On the approximate controllability of Stackelberg-Nash strategies. In: Díaz JI, editor. Ocean circulation and pollution control mathematical and numerical investigations. Berlin: Springer; 2005. p. 17–27]; 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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Acknowledgements
The authors want to express their gratitude to the anonymous reviewers for their questions and commentaries since they were very helpful in improving this article.