Skip to content
DraconiticResearch
Search Sources API
206,690 studies31 sourcesUpdated 18 min ago
PreprintarXiv licencearXiv

Minimal null control time of some 1D linear hyperbolic balance laws with constant coefficients and properties of related kernel equations

  • Long Hu
  • Guillaume Olive
Open at sourcePDFDOICite

Abstract

In this work, we study the null controllability by one-sided boundary controls of one-dimensional hyperbolic balance laws with constant coefficients. Our first result shows that, when the system has only one negative or positive speed, the minimal null control time of such systems depends on some orthogonality conditions for a particular sequence. This sequence is explicit in function of the coefficients of the system but it is defined by a nonlinear recurrence relation. Our second result then completes the previous one by giving explicit bounds on the number of orthogonality conditions that have to be checked in two nontrivial situations. The proofs rely on a careful analysis of the so-called kernel equations associated with the system, including a new well-posedness result. Our results are also valid for the finite-time stabilization property.

Versions

Related

  1. Model-based clustering of diffusion processes with constant volatility coefficients using high-frequency data
    Shogo Kusano, Masayuki Uchida
    arXivPreprintarXiv licenceFull textStatisticsarXiv
  2. Loss of derivatives for hyperbolic operators with coefficients oscillating in time
    Wenhui Chen, Michael Reissig
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  3. Constant mean curvature disks with circular boundary in the $3$-sphere and in hyperbolic space
    Rafael López
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  4. The best Ulam constant of the n-th order linear differential operator with constant coefficients
    Jawad Boutarfass, Iz-iddine EL-Fassi, Lahcen Oukhtite
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  5. SIMULTANEOUS RECOVERY OF VARIOUS TIME-DEPENDENT COEFFICIENTS IN A HYPERBOLIC EQUATION WITH SPACE-TIME NONLOCAL ATTENUATION
    Yavar Kian, Gunther Uhlmann
    HALPreprintCC BY-NC 4.0Full textAnalysis & PDEsHALarXiv

Cite

BibTeXRIS
BibTeX
@misc{hu2026minimal,
  title = {{Minimal null control time of some 1D linear hyperbolic balance laws with constant coefficients and properties of related kernel equations}},
  author = {Long Hu and Guillaume Olive},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.11118},
  eprint = {2609.11118},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11118},
}
RIS
TY  - UNPB
TI  - Minimal null control time of some 1D linear hyperbolic balance laws with constant coefficients and properties of related kernel equations
AU  - Long Hu
AU  - Guillaume Olive
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.11118
UR  - https://arxiv.org/abs/2609.11118
AB  - In this work, we study the null controllability by one-sided boundary controls of one-dimensional hyperbolic balance laws with constant coefficients. Our first result shows that, when the system has only one negative or positive speed, the minimal null control time of such systems depends on some orthogonality conditions for a particular sequence. This sequence is explicit in function of the coefficients of the system but it is defined by a nonlinear recurrence relation. Our second result then completes the previous one by giving explicit bounds on the number of orthogonality conditions that have to be checked in two nontrivial situations. The proofs rely on a careful analysis of the so-called kernel equations associated with the system, including a new well-posedness result. Our results are also valid for the finite-time stabilization property.
ER  -