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PreprintCC BY 4.0arXiv

Hierarchical local null controllability for a non-degenerate quasi-linear parabolic system

  • Cristian Loli
  • George J. Bautista
  • Juan Limaco
  • Rafael Lobosco
  • Dany Nina-Huaman
  • Luis P. Yapu
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Abstract

In this manuscript, we are concerned with the hierarchical control of a non-degenerate quasi-linear parabolic system, posed on a bounded interval. We use the Stackelberg-Nash strategy with a single control called leader and two controls called followers. First, we study the controllability for the linear system, where we will demonstrate a Carleman inequality associated with the adjoint problem. Then, using the results obtained for the linear case and applying Liusternik's Inverse Function Theorem, we obtain local null controllability for the quasi-linear problem.

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Cite

BibTeXRIS
BibTeX
@misc{loli2026hierarchical,
  title = {{Hierarchical local null controllability for a non-degenerate quasi-linear parabolic system}},
  author = {Cristian Loli and George J. Bautista and Juan Limaco and Rafael Lobosco and Dany Nina-Huaman and Luis P. Yapu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.24379},
  eprint = {2608.24379},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.24379},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Hierarchical local null controllability for a non-degenerate quasi-linear parabolic system
AU  - Cristian Loli
AU  - George J. Bautista
AU  - Juan Limaco
AU  - Rafael Lobosco
AU  - Dany Nina-Huaman
AU  - Luis P. Yapu
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2608.24379
UR  - https://arxiv.org/abs/2608.24379
AB  - In this manuscript, we are concerned with the hierarchical control of a non-degenerate quasi-linear parabolic system, posed on a bounded interval. We use the Stackelberg-Nash strategy with a single control called leader and two controls called followers. First, we study the controllability for the linear system, where we will demonstrate a Carleman inequality associated with the adjoint problem. Then, using the results obtained for the linear case and applying Liusternik's Inverse Function Theorem, we obtain local null controllability for the quasi-linear problem.
ER  -