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Periodic KPP equations in hyperbolic space
Abstract
We study Fisher-KPP equations on hyperbolic space with reactions periodic in a Busemann coordinate or in the distance from a point or a geodesic. We determine spectral thresholds for extinction and persistence, including critical extinction from L2 data, and characterize the signed speeds of horospherical fronts. In the hyperbolic plane, we construct a smooth periodic reaction admitting a positive stationary solution that decays away from a geodesic, and determine the spreading speed along the geodesic. For constant linear growth, we obtain logarithmic level positions with bounded error for balls, horoballs and geodesic tubes.
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BibTeX
@misc{hu2026periodic,
title = {{Periodic KPP equations in hyperbolic space}},
author = {Yuanyang Hu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02923},
eprint = {2611.02923},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02923},
}
RIS
TY - UNPB
TI - Periodic KPP equations in hyperbolic space
AU - Yuanyang Hu
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.02923
UR - https://arxiv.org/abs/2611.02923
AB - We study Fisher-KPP equations on hyperbolic space with reactions periodic in a Busemann coordinate or in the distance from a point or a geodesic. We determine spectral thresholds for extinction and persistence, including critical extinction from L^2 data, and characterize the signed speeds of horospherical fronts. In the hyperbolic plane, we construct a smooth periodic reaction admitting a positive stationary solution that decays away from a geodesic, and determine the spreading speed along the geodesic. For constant linear growth, we obtain logarithmic level positions with bounded error for balls, horoballs and geodesic tubes.
ER -