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Boundary approximate controllability of some linear parabolic systems

  • Guillaume Olive
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Abstract

This paper focuses on the boundary approximate controllability of two classes of linear parabolic systems, namely a system of n heat equations coupled through constant terms and a 2 × 2 cascade system coupled by means of a first order partial differential operator with space-dependent coefficients. For each system we prove a sufficient condition in any space dimension and we show that this condition turns out to be also necessary in one dimension with only one control. For the system of coupled heat equations we also study the problem on rectangle, and we give characterizations depending on the position of the control domain. Finally, we exhibit a cascade system for which the distributed controllability holds whereas the boundary controllability does not. The method relies on a general characterization due to H.O. Fattorini.

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Cite

BibTeXRIS
BibTeX
@misc{olive2026boundary,
  title = {{Boundary approximate controllability of some linear parabolic systems}},
  author = {Guillaume Olive},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.09982},
  eprint = {2609.09982},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.09982},
}
RIS
TY  - UNPB
TI  - Boundary approximate controllability of some linear parabolic systems
AU  - Guillaume Olive
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.09982
UR  - https://arxiv.org/abs/2609.09982
AB  - This paper focuses on the boundary approximate controllability of two classes of linear parabolic systems, namely a system of n heat equations coupled through constant terms and a 2 × 2 cascade system coupled by means of a first order partial differential operator with space-dependent coefficients. For each system we prove a sufficient condition in any space dimension and we show that this condition turns out to be also necessary in one dimension with only one control. For the system of coupled heat equations we also study the problem on rectangle, and we give characterizations depending on the position of the control domain. Finally, we exhibit a cascade system for which the distributed controllability holds whereas the boundary controllability does not. The method relies on a general characterization due to H.O. Fattorini.
ER  -