Regularity issues for the null-controllability of the linear 1-d heat equation

@article{Micu2011RegularityIF,
  title={Regularity issues for the null-controllability of the linear 1-d heat equation},
  author={Sorin Micu and Enrique Zuazua},
  journal={Systems & Control Letters},
  year={2011},
  volume={60},
  pages={406-413}
}
The fact that the heat equation is controllable to zero in any bounded domain of the euclidean space, any timeT > 0 and from any open subset of the boundary is well known. On the other hand, numerical experiments show the ill-posedness of the problem. In this paper we develop a rigorous analysis of the 1 d problem which provides a sharp description of this ill-posedness. To be more precise, to each initial data y 0 2 L 2 (0; 1) of the 1 d linear heat equation it corresponds a boundary control… CONTINUE READING
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