Skip to content
DraconiticResearch
Search Sources API
186,086 studies31 sourcesUpdated 17 min ago
PreprintarXiv licencearXiv

Periodic Fisher-KPP equations on a regular tree

  • Yuanyang Hu
Open at sourcePDFDOICite

Abstract

We study Fisher-KPP equations on regular trees with reactions periodic in a Busemann coordinate or in distance from a vertex or a bi-infinite geodesic. For nonzero finitely supported data, we characterize the spectral threshold between uniform extinction and persistence, including critical extinction. We establish Bramson corrections for Busemann step data at positive, zero and negative speeds and, above the periodic extinction threshold, for the largest Busemann coordinate and radial level positions of finitely supported solutions. When the periodic spectral minimum is nonpositive but the geodesic spectral threshold is positive, we construct a smallest positive stationary solution with exponential transverse decay, prove uniqueness under an exponential bound, and determine longitudinal spreading with its logarithmic correction. We also classify positive stationary solutions depending only on distance from the geodesic and prove existence and stability results for moving and stationary fronts.

Related

  1. Logarithmic upper bounds and axial front selection for spatially periodic lattice Fisher--KPP equations
    Yuanyang Hu, Zhenkun Wang
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  2. An Upper Bound for the Mean Speed of Transition Fronts and Unbounded Front Widths for Fisher KPP Equations in Almost Periodic Media
    Xing Liang, Linfeng Xu, Qi Zhou +1
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  3. A Kernel Fisher Discriminant Analysis-Based Tree Ensemble Classifier: KFDA Forest
    Donghwan Kim, Seung Hwan Park, Jun‐Geol Baek
    International journal of industrial engineeringPreprintLicence not stated7 citedStatisticsOpenAlex
  4. Quasi-periodic tree sets and structure trees
    Mikael Pichot
    arXivPreprintCC BY 4.0Full textDynamical systemsarXiv
  5. Regular automorphisms of periodic p'-groups need not be splitting
    V. S. Atabekyn
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{hu2026periodic,
  title = {{Periodic Fisher-KPP equations on a regular tree}},
  author = {Yuanyang Hu},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.01842},
  eprint = {2611.01842},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.01842},
}
RIS
TY  - UNPB
TI  - Periodic Fisher-KPP equations on a regular tree
AU  - Yuanyang Hu
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.01842
UR  - https://arxiv.org/abs/2611.01842
AB  - We study Fisher-KPP equations on regular trees with reactions periodic in a Busemann coordinate or in distance from a vertex or a bi-infinite geodesic. For nonzero finitely supported data, we characterize the spectral threshold between uniform extinction and persistence, including critical extinction. We establish Bramson corrections for Busemann step data at positive, zero and negative speeds and, above the periodic extinction threshold, for the largest Busemann coordinate and radial level positions of finitely supported solutions. When the periodic spectral minimum is nonpositive but the geodesic spectral threshold is positive, we construct a smallest positive stationary solution with exponential transverse decay, prove uniqueness under an exponential bound, and determine longitudinal spreading with its logarithmic correction. We also classify positive stationary solutions depending only on distance from the geodesic and prove existence and stability results for moving and stationary fronts.
ER  -