Time-Periodic Chemotaxis in Shifting Environments: Propagation and Planar Forced Waves in RN
Abstract
We study time-periodic Keller--Segel dynamics in a translating KPP environment. In the parabolic--elliptic regime, we prove global boundedness, identify the sharp speed c*=2√(a̅ r̅), establish persistence in the interior region |s|<c*, s· e<c, and derive the complementary sharp upper bounds; for a moving favorable slab, the sign of a principal Floquet exponent determines persistence or extinction under the stated weighted-resolvent condition. For every fixed τ≥0, under constant population diffusivity and sufficiently weak taxis, we further construct locally unique planar forced time-periodic waves in ℝN. The main new analytic mechanisms are an exact Yukawa first-contact estimate, which controls the chemotactic drift at the KPP leading-edge scale without losing the sharp propagation threshold, and a two-sided weighted Fredholm--monodromy continuation framework for the temporally nonlocal signal equation, with explicit control of the far-field spectral gaps and the translational neutral mode. To the best of the author's knowledge, planar forced time-periodic waves in ℝN for shifting Keller--Segel systems have not been investigated in any previous studies; earlier forced-wave results are confined to substantially more restrictive settings, in particular one-dimensional parabolic--elliptic models. Thus the present construction provides the first multidimensional planar forced-wave theory for a time-periodic shifting Keller--Segel system with temporal signal memory.
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BibTeX
@misc{vo2026timeperiodic,
title = {{Time-Periodic Chemotaxis in Shifting Environments: Propagation and Planar Forced Waves in $\R^N$}},
author = {Hoang-Hung Vo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36627},
eprint = {2610.36627},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36627},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Time-Periodic Chemotaxis in Shifting Environments: Propagation and Planar Forced Waves in R^N
AU - Hoang-Hung Vo
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36627
UR - https://arxiv.org/abs/2610.36627
AB - We study time-periodic Keller--Segel dynamics in a translating KPP environment. In the parabolic--elliptic regime, we prove global boundedness, identify the sharp speed c_*=2√(a̅ r̅), establish persistence in the interior region |s|<c_*, s· e<c, and derive the complementary sharp upper bounds; for a moving favorable slab, the sign of a principal Floquet exponent determines persistence or extinction under the stated weighted-resolvent condition. For every fixed τ≥0, under constant population diffusivity and sufficiently weak taxis, we further construct locally unique planar forced time-periodic waves in ℝ^N. The main new analytic mechanisms are an exact Yukawa first-contact estimate, which controls the chemotactic drift at the KPP leading-edge scale without losing the sharp propagation threshold, and a two-sided weighted Fredholm--monodromy continuation framework for the temporally nonlocal signal equation, with explicit control of the far-field spectral gaps and the translational neutral mode. To the best of the author's knowledge, planar forced time-periodic waves in ℝ^N for shifting Keller--Segel systems have not been investigated in any previous studies; earlier forced-wave results are confined to substantially more restrictive settings, in particular one-dimensional parabolic--elliptic models. Thus the present construction provides the first multidimensional planar forced-wave theory for a time-periodic shifting Keller--Segel system with temporal signal memory.
ER -