Generalized Transition Fronts and Spectral Speed Asymptotics in Heterogeneous Cooperative Systems
Abstract
We study generalized transition fronts for cooperative reaction--diffusion systems with spatially periodic and time-dependent coefficients. We obtain sufficient conditions for the existence of fronts and necessary constraints on their propagation speeds in terms of generalized principal eigenvalues. In the almost-periodic case, we identify the two spectral thresholds and examine the attainment of the critical speed under additional hypotheses on the normalized linear evolution. We then investigate the large-advection limit and construct a time-periodic example showing that a stationary spectral characterization need not extend to time-dependent flows. For symmetric cooperative systems in stationary periodic shears with equal diffusion matrices, we obtain explicit correction terms for the minimal speed in both the small- and large-diffusion limits. The two expansions follow from periodic eigenvalue perturbation, localization near a maximal streamline, and minimization over the exponential weight. We also establish a higher-order large-advection expansion and present numerical illustrations independent of the analytic proofs.
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BibTeX
@misc{vo2026generalized,
title = {{Generalized Transition Fronts and Spectral Speed Asymptotics in Heterogeneous Cooperative Systems}},
author = {Hoang-Hung Vo and Cong-Bang Trang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39199},
eprint = {2610.39199},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39199},
}
RIS
TY - UNPB
TI - Generalized Transition Fronts and Spectral Speed Asymptotics in Heterogeneous Cooperative Systems
AU - Hoang-Hung Vo
AU - Cong-Bang Trang
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39199
UR - https://arxiv.org/abs/2610.39199
AB - We study generalized transition fronts for cooperative reaction--diffusion systems with spatially periodic and time-dependent coefficients. We obtain sufficient conditions for the existence of fronts and necessary constraints on their propagation speeds in terms of generalized principal eigenvalues. In the almost-periodic case, we identify the two spectral thresholds and examine the attainment of the critical speed under additional hypotheses on the normalized linear evolution. We then investigate the large-advection limit and construct a time-periodic example showing that a stationary spectral characterization need not extend to time-dependent flows. For symmetric cooperative systems in stationary periodic shears with equal diffusion matrices, we obtain explicit correction terms for the minimal speed in both the small- and large-diffusion limits. The two expansions follow from periodic eigenvalue perturbation, localization near a maximal streamline, and minimization over the exponential weight. We also establish a higher-order large-advection expansion and present numerical illustrations independent of the analytic proofs.
ER -