A free boundary problem for spreading of an invasive species in the territory of a native competitor under shifting climate
Abstract
In this paper we consider a free boundary problem for the spreading of an invasive species in the habitat of a native competitor. We assume that the invasive species benefits from a climate shift that turns the environment from unfavorable to favorable at a constant speed c. We show that if the invasive species is an inferior one, then it must vanish, while the native competitor always persists. However, if the invasive species is a superior one, then a dichotomy occurs: either the invasive species vanishes and the native one persists, or the invasive one spreads and the native one vanishes. We also show that in the latter case the asymptotic spreading speed equals min{c, c0}, where c0 is the spreading speed in the corresponding homogeneous environment. Numerical simulations are provided to illustrate our theoretical results.
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BibTeX
@misc{dinh2026free,
title = {{A free boundary problem for spreading of an invasive species in the territory of a native competitor under shifting climate}},
author = {Phuoc Vinh Dinh and Phuong Le and Tien Dung Nguyen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14573},
eprint = {2609.14573},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14573},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A free boundary problem for spreading of an invasive species in the territory of a native competitor under shifting climate
AU - Phuoc Vinh Dinh
AU - Phuong Le
AU - Tien Dung Nguyen
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14573
UR - https://arxiv.org/abs/2609.14573
AB - In this paper we consider a free boundary problem for the spreading of an invasive species in the habitat of a native competitor. We assume that the invasive species benefits from a climate shift that turns the environment from unfavorable to favorable at a constant speed c. We show that if the invasive species is an inferior one, then it must vanish, while the native competitor always persists. However, if the invasive species is a superior one, then a dichotomy occurs: either the invasive species vanishes and the native one persists, or the invasive one spreads and the native one vanishes. We also show that in the latter case the asymptotic spreading speed equals min{c, c_0}, where c_0 is the spreading speed in the corresponding homogeneous environment. Numerical simulations are provided to illustrate our theoretical results.
ER -