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PreprintCC BY-NC-SA 4.0HAL

Some remarks on the moment method for null controllability of parabolic equations in any dimension

  • Morgan Morancey
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Abstract

This article aims at bringing together some remarks, sometimes elementary, concerning the extension of the construction of biorthogonal families associated with parabolic control problems in any dimension with suitable estimates on the biorthogonal elements. Such construction is well-studied in the one dimensional case but pretty much open in other settings. The goal of this article is not to design such biorthogonal families but to prove that their existence with estimates allowing to solve moment problems is a necessary condition for null controllability to hold for a very large class of parabolic problems. Then, some characterizations of these biorthogonal families are given.

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Cite

BibTeXRIS
BibTeX
@misc{morancey2026some,
  title = {{Some remarks on the moment method for null controllability of parabolic equations in any dimension}},
  author = {Morgan Morancey},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  url = {https://hal.science/hal-05553829v2},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Some remarks on the moment method for null controllability of parabolic equations in any dimension
AU  - Morgan Morancey
PY  - 2026
DA  - 2026/09/24
PB  - HAL
UR  - https://hal.science/hal-05553829v2
AB  - This article aims at bringing together some remarks, sometimes elementary, concerning the extension of the construction of biorthogonal families associated with parabolic control problems in any dimension with suitable estimates on the biorthogonal elements. Such construction is well-studied in the one dimensional case but pretty much open in other settings. The goal of this article is not to design such biorthogonal families but to prove that their existence with estimates allowing to solve moment problems is a necessary condition for null controllability to hold for a very large class of parabolic problems. Then, some characterizations of these biorthogonal families are given.
ER  -